Class Of Semigroups Research Articles

Certified Severi dimensions for hyperelliptic and supersymmetric cusps

In a previous paper, the first three authors formulated a precise conjecture about the dimension of the generalized Severi varietyMd,g;S,kn of degree-d holomorphic maps P1→Pn whose images' singularities are singleton cusps with value semigroups S and ramification profiles k. In this paper, we prove that an adjusted form of the conjecture holds for generic profiles k associated with two distinguished (infinite) classes of semigroups S.

The Relationship betweenE-Semigroups andR-Semigroups

A semigroup is called anE-semigroup (R-semigroup) if the set of all idempotents (the set of all regular elements) forms a subsemigroup. In this paper, we introduce the concept ofV-semigroups and establish the relationship between the three classes of semigroups.

Categories and semigroups

The aim of this paper is to consider the correspondence between the classification of morphisms in categories and the classes of semigroups with idempotents, in particular, we establish a mutual corresponding theorem of three classes of categories and the classes of left (right) abundant, two-sided abundant semigroups and regular semigroups. We first apply the nine axioms (P1)–(P9) which characterize cancellation and split properties of morphisms in a category to classify categories into three subclasses: idempotent ample ([Formula: see text]-, for short) categories, balanced categories and normal categories. The intrinsic relationship between these categories and their cone semigroups is investigated. It is proved that the cone semigroup of an [Formula: see text]-category is left abundant and vice versa, the category of principal left ∗-ideals of a left abundant (not necessarily right abundant) semigroup is an [Formula: see text]-category. Similar results for balanced categories and abundant semigroups are reproved and strengthened. As a consequence, we employ categorical terms to characterize those abundant semigroups in which the regular elements form a regular subsemigroup. Therefore, the significant theory of normal categories and regular semigroups devoted by K. S. S. Nambooripad is generalized to arbitrary abundant semigroups and even to left and right abundant semigroups, respectively.

On the class semigroup of root-closed weakly Krull Mori monoids

On the class semigroup of root-closed weakly Krull Mori monoids

On characterisations of certain classes of semigroups

On characterisations of certain classes of semigroups

On radicals in a certain class of semigroups

On radicals in a certain class of semigroups

On relatively elementary definability of graph classes in the class of semigroups

On relatively elementary definability of graph classes in the class of semigroups

Строение наследственно чистых полугрупп с центральным идемпотентом

A description is given of hereditarily pure semigroups in the class of semigroups with distinguished central idempotent.

Relatively Elementary Definability of the Class of Universal Graphic Semiautomata in the Class of Semigroups

Relatively Elementary Definability of the Class of Universal Graphic Semiautomata in the Class of Semigroups

Conjugacy classes of left ideals of Sweedler's four-dimensional algebra $ H_{4} $

<abstract><p>Let $ A $ be a finite-dimensional algebra with identity over the field $ \mathbb{F} $, $ U(A) $ be the group of units of $ A $ and $ L(A) $ be the set of left ideals of $ A $. It is well known that there is an equivalence relation $ \sim $ on $ L(A) $ by defining $ L_1\sim L_2\in L(A) $ if and only if there exists some $ u\in U(A) $ such that $ L_{1} = L_{2}u $. $ C(A) = \{[L]|L\in L(A)\} $ is the set of equivalence classes determined by the relation $ \sim $, which is a semigroup with respect to the natural operation $ [L_1][L_2] = [L_1L_2] $ for any $ L_1, L_2 \in L(A) $. The purpose of this paper is to describe the structures of semigroup of conjugacy classes of left ideals for the Sweedler's four-dimensional Hopf algebra $ H_{4} $.</p></abstract>

On lattice isomorphisms of orthodox semigroups

Two semigroups are lattice isomorphic if the lattices of their subsemigroups are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups in which every nonidempotent element has infinite order is lattice closed.

On infinite extensions of Dedekind domains, upper semicontinuous functions and the ideal class semigroups

We study the monoid of fractional ideals and the ideal class semigroup of an arbitrary given one dimensional normal domain 𝔒 obtained by an infinite integral extension of a Dedekind domain. We introduce a notion of “upper semicontinuous functions” whose domain is the maximal spectrum of 𝔒 equipped with the inverse topology introduced by Hochster, and whose codomain is a certain totally ordered monoid containing ℝ. We construct an isomorphism between a monoid consisting of such upper semicontinuous functions satisfying certain conditions and the monoid of fractional ideals of 𝔒. This result can be regarded as a generalization of the theory of prime ideal factorization for Dedekind domains. By using such isomorphism, we study the Galois-monoid structure of the ideal class semigroup of 𝔒.

Riemann bm$\zeta$-functions on semigroups

By introducing prime elements in semigroups, divisor functions and Möbius functions are defined and studied on a class of semigroups. The Riemann $\\zeta$-function can be naturally generalized through different means on these semigroups. The semigroup associated with Thompsons group is a typical example of our interest. We show that zeta functions on Thompsons semigroup obtained through different definitions agree with each other. Moreover, this zeta function has at least another real pole less than 1 besides a simple pole at 1. Many other arithmetic results are obtained on some noncommutative semigroups such as analogs of the prime number theorem on natural numbers.

On the Artin Semigroups

This paper introduces the concept of the Artin semigroup of a large (extra large) type. We prove their injective embedding in the corresponding Artin groups of large (extra large) type and the solvability of the word conjugacy problem in this class of semigroups.

Log-convex set of Lindblad semigroups acting on N-level system

We analyze the set ANQ of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an N-level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set ANQ is shown to be log-convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels, the super-decoherence commutes with the dynamics so that decohering a quantum accessible channel, we obtain a bistochastic matrix from the set ANC of classical maps accessible by a semigroup. Focusing on three-level systems, we investigate the geometry of the sets of quantum accessible maps, its classical counterpart, and the support of their spectra. We demonstrate that the set A3Q is not included in the set U3Q of quantum unistochastic channels, although an analogous relation holds for N = 2. The set of transition matrices obtained by super-decoherence of unistochastic channels of order N ≥ 3 is shown to be larger than the set of unistochastic matrices of this order and yields a motivation to introduce the larger sets of k-unistochastic matrices.

Boolean Zero Square (BZS) Semigroups

We introduce a new class of semigroups, that we call BZS - Boolean Zero Square-semigroups. A semigroup S with a zero element, 0, is said to be a BZS semigroup if, for every , we have or . We obtain some properties that describe the behaviour of the Green’s equivalence relations , , and . Necessary and sufficient conditions for a BZS semigroup to be a band and an inverse semigroup are obtained. A characterisation of a special type of BZS completely 0-simple semigroup is presented.

About the class of approximation by generalized characters

Given a certain class K1 of algebraic structures. We study a problem of finding a class K2 of algebraic structures such that the class K1 is approximable into K2 with respect to various predicates by generalized characters from K1 to K2. The problem of minimization of approximation is also considered. Some theorems related to the problem of constructing an approximation class are obtained. The problem in question is much more complicated and actual than the approximation problem we have been studying before (see [2]-[6]). The results of the description of the approximation class play an important role in studying the solvability problem of the predicate P in the class of semigroups K. In particular, if the approximation class consists of finite semigroups, then this problem is solved positively. Even more difficult is the problem of determining the necessary conditions that class is an approximation class for a given class K.

Generalized Hesitant Fuzzy Ideals in Semigroups

In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals (resp. 0 , n -ideals) are introduced. Furthermore, conditions for a hesitant fuzzy m , n -ideal ( m , 0 -ideal, 0 , n -ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy m , n -ideals ( m , 0 -ideals, 0 , n -ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals ( 0 , n -ideals) are investigated.

English

We explore the connection between atomicity in Prufer domains and their corresponding class groups. We observe that a class group of infinite order is necessary for non-Noetherian almost Dedekind and Prufer domains of finite character to be atomic. We construct a non-Noetherian almost Dedekind domain and exhibit a generating set for the ideal class semigroup.

The Structure of Regular Right Uniform Semigroups

In this paper, we investigate the right uniform notion on some classes of semigroups. The main objective of this paper is identifying the structure of regular right uniform semigroups which can be applied as a cornerstone of characterizing regular right subdirectly irreducible semigroups.