Pure Ideals Research Articles

Strongly pure ideals

Strongly pure ideals

“Passionate Protest”:The Value Choice of Chinese Students Studying in the United States to“Resist Japanese Goods” under the“Shandong Issue”

After the failure of China's negotiations at the Paris Peace Conference in 1919, a fierce national consciousness quickly spread to the entire intellectual community, especially among Chinese students in the United States, who remained intensely national even though they were on the other side of the ocean. Under the stimulation of domestic and foreign difficulties, the call for national salvation is increasingly rising, and the connection between“scholar” and“national salvation” has become close, and many students consciously take the mission of national salvation to themselves. Students in the United States expressed their close attention to this situation through the“passionate revolution” of“boycotting Japanese goods”. For the students studying in the United States, although they live on the other side of the ocean, the number is not large compared with the vigorous protests in China, but they inevitably participate in the tide of national salvation and become one of the important forces for national salvation. In terms of the attitude of foreign students to“boycott Japanese goods”, most of them have a deep-rooted national consciousness in China since ancient times, while a minority of them, as representatives, are more inclined to adopt a way of self-improvement that tends to“national self-determination” and has more internal awareness of the nation. Reflects the scholar to serve the country another face. It can be said that the value choices and a series of historical activities of students studying in the United States driven by patriotic spirit reflect the dual interaction between students studying in the United States and the fate of the country in modern times, and shine the light of pure patriotic ideals of overseas students on the other side.

Characterizations of regular and k-regular semirings by pure ideals and pure k-ideals

Characterizations of regular and k-regular semirings by pure ideals and pure k-ideals

다자이 오사무(太宰治) 「토카톤톤(トカトントン)」에 나타난 모순의 구조 - 다자이 오사무의 전후 인식을 중심으로 -

Osamu Dazai’s (太宰治) Tokatonton(トカトントン) novel was published in Volume 2, Issue 1 of Gunzō (群像), on January 1, 1947. The novel is written in an epistolary format, where a 26-year-old young man complains to a certain writer about the pain of hearing a hammering sound and losing motivation, every time he tries to focus on something. The present paper contemplates Dazai’s post-war perceptions, after examining issues of post-war Japan’s ambivalence, desire for innocence, and expressions of irony, with a focus on the logical contradictions revealed in Tokatonton. Japan’s defeat in the war, brought about a surging desire to overcome the past and build a new Japan. This contradicted with those who wanted to go against the times and continue fighting. To the Japanese people, Japan’s defeat also meant liberation and freedom from the oppression of militarism. However, even after the defeat, the General Head Quarters (GHQ) ruthlessly censored creative works that went against the occupation policy. The issues that the young man in Tokatonton want to focus on, such as ‘writing novels,’ ‘post office work,’ ‘dating,’ ‘workers’ demonstrations,’ ‘sports,’ and ‘black market dealings,’ symbolize the misaligned post-war space. The young man’s frustration itself is ‘post-war frustration,’ which symbolizes the same. Hence, the method of expressing post-war Japan’s two sides in Tokatonton is similar to the method of expressing ‘irony’ in Japanese Romanticism, where Osamu Dazai had once participated. It can be said that, Osamu Dazai’s ‘ironic’ expressions have the structure in which, the side revealed openly and its opposing hidden side, reveal themselves cyclically, thus making it impossible to know the truth. For Dazai, Japan’s post-war space was ironic and impossible to interpret, with coexisting freedom and oppression. The hope of building a new Japan and the pitiful reality that did not match, neither did the pure ideals and the ‘dirty’ worldliness.

On Tripolar Fuzzy Pure Ideals in Ordered Semigroups

Tripolar fuzzy sets are a concept that deals with tripolar information. This idea is a generalization of bipolar and intuitionistic fuzzy sets. In this paper, the notions of tripolar fuzzy pure ideals in ordered semigroups are introduced, and some algebraic properties of tripolar fuzzy pure ideals are studied. We obtain some characterizations of weakly regular ordered semigroups in terms of tripolar fuzzy pure ideals. Finally, we introduce the concepts of tripolar weakly pure ideals and prove that the tripolar fuzzy ideals are tripolar weakly pure ideals if such tripolar fuzzy ideals satisfy the idempotent property.

Psychoanalyzing democracies: Antagonisms, paranoia, and the productivity of depression

Psychoanalyzing democracies: Antagonisms, paranoia, and the productivity of depression

아도르노(Adorno)의 "교직의 터부"를 통해 본 교사전문성의 의미

The purpose of this study is to reveal the limits of teacher expertise by examining the specific historical and social conditions in which the teaching profession is located. To this end, the discussion of the taboos of Adorno's teaching profession is the center of the study. Adorno sees the image that makes it impossible for teachers to independently perform their jobs as taboos, and grasps the appearance of taboos in the teaching profession as a social condition and the causes of its formation from a historical and Freudian psychoanalytic perspective. The point to be emphasized here is that Adorno is the taboo of the teaching profession, that is, the deceptive social system that forces students to mediate civilization through education through consideration of the ambivalence of the teaching profession, and the tragic situation the teacher is in as a psychological and social agent, that is, the teaching profession. Therefore, the researchers first examine the history of the teaching profession in Germany and Europe in detail in order to reveal that the negative image of teachers has been historically formed. Next, based on Freud's libido, Oedipus complex, and superego concept, the process by which the taboo of the teaching profession was established as a social prejudice is considered psychoanalytically. Through this, the values, norms, and behaviors of society that teachers pass on to their students, that is, civilization, allow students to experience alienation. In the end, it is difficult for teachers to realize the content delivered through the act of teaching, which is one of their pure educational ideals and values. Therefore, this study aims to stimulate teachers' self-reflection by making them doubt their confidence in the teacher's professionalism.

Some Results on Pure Ideals and Trace Ideals of Projective Modules

Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if and only if Ann(f) + I = R for all f ∈ I. If J is the trace of a projective R-module M, we prove that J is generated by the “coordinates” of M and JM = M. These lead to a few new results and alternative proofs for some known results.

The prime and maximal spectra and the reticulation of residuated lattices with applications to De Morgan residuated lattices

Abstract In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices they become compact T 0 {T}_{0} topological spaces. At the same time, we define and study the reticulation functor between De Morgan residuated lattices and bounded distributive lattices. Moreover, we study the I-topology (I comes from ideal) and the stable topology and we define the concept of pure ideal. We conclude that the I-topology is in fact the restriction of Zariski topology to the lattice of ideals, but we use it for simplicity. Finally, based on pure ideals, we define the normal De Morgan residuated lattice (L is normal iff every proper ideal of L is a pure ideal) and we offer some characterizations.

On ideals of rings of continuous functions associated with sublocales

Let X be a Tychonoff space. Associated with every subset A⊆βX is the ideal OA of the ring C(X) consisting of all functions that vanish in a neighborhood of X∩A. Now, viewing Tychonoff spaces as objects in the category CRLoc of completely regular locales, we have ideals of the form OA, where A is a sublocale of βX. In this paper we study properties of such ideals not only for Tychonoff spaces, but for any object in CRLoc. Carrying out the discussion in this category, we have more function rings (they are denoted RL, for any L∈CRLoc) than the class of the rings C(X). Pure ideals of C(X) are known to be exactly the ideals OA, for A a closed subset of βX. We characterize the spaces for which the ideals OA, for A a closed subset of X (note that it need not be closed in βX) are pure ideals. They properly contain the normal ones. We describe the socle of any ring RL as the ideal OA, with A equal to the join of all nowhere dense sublocales of βL. We show that the socle is zero precisely when βL is dense in itself, and essential if and only if the smallest dense sublocale of βL has a complement in the lattice of sublocales of βL. If βL is scattered, then this is so if and only if L has a smallest nowhere dense sublocale.

Characterizations of Gelfand Rings Specially Clean Rings and their Dual Rings

In this paper, new criteria for zero dimensional rings, Gelfand rings, clean rings and mp-rings are given. A new class of rings is introduced and studied, we call them purified rings. Specially, reduced purified rings are characterized. New characterizations for pure ideals of reduced Gelfand rings and mp-rings are provided. It is also proved that if the topology of a scheme is Hausdorff, then the affine opens of that scheme is stable under taking finite unions. In particular, every compact scheme is an affine scheme.

Design with Fourth Nature

This article posits designing with Fourth Nature as an alternative to dominant modes of practice in restoration ecology, heritage management and landscape architecture. We explore the contours of resistance in these fields to Fourth Nature landscapes, questioning how we might move past static and pure ideals while remaining in dialogue with the rich history of garden and landscape design. We explore why recent developments in the ecological sciences have not been more widely adopted in landscape architecture practices in the United States. Our approach questions long-held perceptions of appropriate plant assemblages and presents alternatives for managing eco-systems at historically layered landscapes where restoration of the historical reference is not practical or possible. We call for extending understandings of Fourth Nature into a framework for designed landscapes that goes beyond wildlands and spontaneous plants. This approach translates ecological values into a design language that is dynamic and process-oriented.

On the maximal regular ideal of pointfree function rings, and more

Let L be a completely regular frame and, as customary, let RL denote the ring of continuous real-valued functions on L. In the first part of the paper we characterize the maximal regular ideal of RL. We show that it consists precisely of the functions α such that the open sublocale of L associated with coz α is clopen and is a P-frame. We also give a characterization of this ideal in terms of the notion of the localic remainder. In contrast, the maximal regular ideal of the ring ZL of continuous integer-valued functions on L is shown to be always the zero ideal. Purity and regularity of ideals are germane in the description and characterization of the maximal regular ideal of RL. It is for this reason that in the last part of the paper we consider ideals of ideals of RL because, as we prove, it is precisely the pure ideals of RL all of whose ideals are ideals in the whole ring.

A “WHITE BOY . . . WHO IS NOT A WHITE BOY”: RUDYARD KIPLING'S KIM, WHITENESS, AND BRITISH IDENTITY

Rudyard Kipling's final novel, Kim (1901), begins with an intriguing – if paradoxical – description of the eponymous Kim, or Kimball O'Hara: he is an “English” boy with an Irish name and Irish parentage who speaks “the [Indian] vernacular by preference” (1). While the narrator hastens to reassure the reader that Kim is both “white” and “English,” Kim is also “burned black as any native” and speaks his supposed “mother tongue,” English, in an “uncertain sing-song” (1). If we are to take Kipling's assertion at face value, that Kim is, indeed, “English,” then certainly this is a kind of Englishness that is divorced completely from the racially pure ideals of Anglo-Saxon whiteness that were privileged by many racial theorists earlier in the nineteenth century. As an Irish Celt, Kipling's protagonist is always already at a layer of remove from ideals of pure Englishness, but Kipling renders Kim's racial identity even more complicated in the text. The manuscript of Kim gives us some telling clues about the contexts that inform Kipling's peculiar descriptions of “burned black” whiteness in his finished novel. While the published text baldly declares that “Kim was English. . . . Kim was white” (1; ch. 1; emphasis mine), parts of the manuscript are much less certain of this fact, as that document asserts that Kim “looked like a half caste” (Kipling, Kim o’ the ‘Rishti n. 3). And while Kipling ultimately removed this explicit link between Kim and Eurasian bodies in the opening of his published text, this disavowal is neither complete nor convincing throughout Kim. For instance, in the novel, the narrator later describes a “half-caste woman who looked after [Kim . . . and] told the missionaries that she was Kim's mother's sister” (1; ch. 1). While this woman is not, in fact, the boy's aunt, Kim's near-familial tie with her underlines the intimate connection between him and the hybridized subjects of empire. Indeed, Kim demonstrates ideological and affective links to non-white Others and to people of mixed race, and this connection between whiteness and racial hybridity is of central importance to Kipling. If Kim is tenuously white, then he can only perform this whiteness in immediate proximity to racial hybridity, with which whiteness is ideologically contiguous in this text. As I contend in this paper, Kim reveals the under-examined links between early twentieth-century ideas of white British identity and descriptions of imperial miscegenation. In Kim, “White” and “English” emerge as a vexed pair of signifiers that reveal unprecedented traces of racial and national hybridization.

The Forgetting of Cora Wilburn: Historical Amnesia and The Cambridge History of Jewish American Literature

The Forgetting of Cora Wilburn: Historical Amnesia and <i>The Cambridge History of Jewish American Literature</i>

A is for Aria

A is for Aria

Local 𝔪-adic constancy of F-pure thresholds and test ideals

AbstractIn this paper, we consider a corollary of the ACC conjecture for F-pure thresholds. Specifically, we show that the F-pure threshold (and more generally, the test ideals) associated to a polynomial with an isolated singularity are locally constant in the 𝔪-adic topology of the corresponding local ring. As a by-product of our methods, we also describe a simple algorithm for computing all of the F-jumping numbers and test ideals associated to an arbitrary polynomial over an F-finite field.

A short note on a generalization of pure ideals in commutative semigroups

A short note on a generalization of pure ideals in commutative semigroups

On regular ideals in reduced rings

Let R be a commutative ring with identity and X be a Tychonoff space. An ideal I of R is Von Neumann regular (briefly, regular) if for every a ? I, there exists b ? R such that a = a2b. In the present paper, we obtain the general form of a regular ideal in C(X) which is OA, for some closed subset A of ?X, for which Ac?X ? (P(X))?, where P(X) is the set of all P-points of X. We show that the ideals and subrings such as CK(X), C?(X), C?(X), SocmC(X) and M?X\X are regular if and only if they are equal to the socle of C(X). We carry further the study of the maximal regular ideal, for instance, it is shown that for a vast class of topological spaces (we call them OPD-spaces) the maximal regular ideal is OX\I(X), where I(X) is the set of isolated points of X. Also, for this class, the socle of C(X) is the maximal regular ideal if and only if I(X) contains no infinite closed set. We also show that C(X) contains an ideal which is both essential and regular if and only if (P(X))? is dense in X. Finally it is shown that, for semiprimitive rings pure ideals are of the form OA which A is a closed subset of Max(R), also a P-point of X = Max(R) is introduced and it is shown that the maximal regular ideal of an arbitrary ring R is OX\P(X), which P(X) is the set of P-points of X = Max(R).

P-ideals and PMP-ideals in Commutative rings

Recently, P-ideals studied in ${\rm C}(X)$ by some authors. In this article we investigate {\rm P}-ideals and a new concept as PMP-ideals in commutative rings. We show that $I$ is a {\rm P}-ideal (resp., {\rm PMP}-ideal) in $R$ if and only if every prime ideal of $R$ which does not contain $I$ is a maximal (resp., minimal prime) ideal of $R$. Also, we characterize largest {\rm P}-ideals (resp., PMP-ideals) in commutative rings, specially in ${\rm C}(X)$. Furthermore, we study relation between these ideals and pure ideals. %\end{abstract} Finally we prove that ${\rm C}(X)$ is a von Neumann regular ring if and only if every pure ideal of it is P-ideal.