Ideals In Semigroups Research Articles

Ideals in semigroups of partial transformations with invariant set

Ideals in semigroups of partial transformations with invariant set

Some Approximate Division and Semigroup Identities for the Mittag-Leffler Function

It is known that the Mittag-Leffler (ML) function, Eα(z), a non-local extension of the Euler exponential function ez, does not enjoy the semigroup property while ez does. The purpose of this note is to show that Eα(z) does, however, for real t, s with s small enough, enjoy the approximate semigroup property, Eα(t+s)≈Eα(t)(1+Eα,α(t)/Eα(t))s. This follows from an approximation of limh→0+Eα(±(u+h)α)/Eα(±uα) , which also yields related expressions for α→1−, and is obtained from a recently proposed universal difference quotient representation for fractional derivatives. Graphical demonstrations are presented to show that the approximations are 'reasonably accurate' for 0h≤0.1, with virtually no distinction from identity for 0h≤0.01.

Identities of Hecke–Kiselman monoids

AbstractIt is shown that the Hecke–Kiselman monoid $${\text {HK}}_{\Theta }$$ HK Θ associated to a finite oriented graph $$\Theta $$ Θ satisfies a semigroup identity if and only if $${\text {HK}}_{\Theta }$$ HK Θ does not have free noncommutative subsemigroups. It follows that this happens exactly when the semigroup algebra $$K[{\text {HK}}_{\Theta }]$$ K [ HK Θ ] over a field K satisfies a polynomial identity. The latter is equivalent to a condition expressed in terms of the graph $$\Theta $$ Θ . The proof allows to derive concrete identities satisfied by such monoids $${\text {HK}}_{\Theta }$$ HK Θ .

Soft intersection almost ideals of semigroups

The aim of this study is to present the notion of soft intersection almost left (respectively, right) ideal of a semigroup which is a generalization of nonnull soft intersection left (respectively, right) ideal of a semigroup and investigate the related properties in detail. We show that every idempotent soft intersection almost (left/right) ideal is a soft intersection almost subsemigroup. Besides, we acquire remarkable relationships between almost left (respectively, right) ideals and soft intersection almost left (respectively, right) ideals of a semigroup as regards minimality, primeness, semiprimeness and strongly primeness.

A Study of Fuzzy Prime Near-rings Involving Fuzzy Semigroup Ideals

In this paper, our main objective is to introduce the notion of a fuzzy semigroup ideal by using Yuan and Lee's definition of fuzzy group based on fuzzy binary operations. Also, some of its basic properties are studied analogously to the known results in the case of semigroup ideals defined in the framework of ordinary near-rings.

SEMI GROUP IDENTITIES WITH APPLICATIONS TO SEMI GROUPS

This research paper explores the rich and intriguing world of semi-group identities, their properties, and their applications to various types of semi-groups. Semi-groups are algebraic structures that generalize the notion of groups, allowing for non-invertible elements. Despite their broader scope, semi-groups retain many important features found in group theory. This study investigates the identities that hold true in the context of semi-group algebra and sheds light on the underlying mathematical structures and relationships among these identities. By delving into specific applications, we illustrate the significance of these findings to various types of semi-groups, such as monoids, semigroups with zero, and cancellative semi-groups. Ultimately, our results not only deepen our understanding of the fundamental properties of semi-groups. But also provide valuable insights for researchers in the areas of algebraic structures, combinatorics, and theoretical computer science.

A Study on Rough Fuzzy Bipolar Soft Ideals in Semigroups

The theories of rough sets (RSs) and soft sets (SSs) are practical mathematical techniques to accommodate data uncertainty. On the other hand, fuzzy bipolar soft sets (FBSSs) can address uncertainty and bipolarity in various situations. The key objective of this study is to establish the notions of rough fuzzy bipolar soft ideals in semigroup (SG), which is an extension of the idea of rough fuzzy bipolar soft sets in a SG. Also, we have analyzed the roughness in the bipolar fuzzy subsemigroup (BF-SSG) by employing a congruence relation (CR) defined on the SG and investigating several related characteristics. Further, the idea is expanded to the rough fuzzy bipolar soft ideal, rough fuzzy bipolar soft interior ideal, and rough fuzzy bipolar soft bi-ideal in SGs. Moreover, it is observed that CR and complete CR (CCR) are critical in developing rough approximations of fuzzy bipolar soft ideals. Therefore, their related characteristics are studied via CRs and CCRs.

Enhanced Characterization of Rough Semigroup Ideals: Extension and Analysis

Enhanced Characterization of Rough Semigroup Ideals: Extension and Analysis

Generalized interval valued fuzzy ideals in semigroups

Generalized interval valued fuzzy ideals in semigroups

Applications of Bipolar Fuzzy Almost Ideals in Semigroups

In this paper, we give the concept of bipolar fuzzy almost ideal, minimal almost bipolar fuzzy ideals, and prime (semiprime, strongly prime) bipolar fuzzy almost ideals in semigroups. We investigate the basic properties of bipolar fuzzy almost ideals in semigroups. Finally, we study the relationship between almost ideals and bipolar fuzzy almost ideals in semigroups.

On picture fuzzy almost ideals of semigroups

In this paper, we give the concept of picture fuzzy almost ideals, minimal picture fuzzy almost ideals, and prime (semiprime, strongly prime) picture fuzzy almost ideals in semigroups. We prove the basic properties of picture fuzzy almost ideals in semigroups. Moreover, we investigate the connection between almost ideals and picture fuzzy almost ideals in semigroups.

Tri-quasi Ideals and Fuzzy Tri-quasi Ideals of Semigroups

Tri-quasi Ideals and Fuzzy Tri-quasi Ideals of Semigroups

Tri-quasi Ideals and Fuzzy Tri-quasi Ideals of Semigroups

Tri-quasi Ideals and Fuzzy Tri-quasi Ideals of Semigroups

Some Properties of Fuzzy Ideals of Unit Regular Semigroups

This paper introduces the concept of unit-regular fuzzy ideals of semi groups, which is a generalization of regular fuzzy ideals. Several of their significant related properties have been examined. According to the unit-regular semi group, the fuzzy-interior-ideal, fuzzy-ideal, fuzzy-bi-ideal, and fuzzy-generalized-bi-ideal have all been described.

Almost bi-quasi-ideals and their fuzzifications in semigroups

The notion of bi-quasi-ideals of semigroups was introduced by Krishna Rao in 2017, which is a generalization of left ideals, right ideals, bi-ideals, and quasi-ideals of semigroups. In this paper, we introduce the concept of almost bi-quasi ideals as a generalization of bi-quasi ideals of semigroups. We investigate the properties of almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals in semigroups. Moreover, we show some relationships between almost bi-quasi-ideals and fuzzy almost bi-quasi-ideals.

General types of sup -hesitant fuzzy ideals of ternary semigroups

General types of sup -hesitant fuzzy ideals of ternary semigroups

Spherical interval valued fuzzy ideals which coincide in semigroups

The concept of spherical fuzzy set was introduced by Gun et al. in 2018. It is generalization of Pythagorean fuzzy set. Our main paper, we give the concepts of spherical interval valued fuzzy ideals in semigroups, and properties of a spherical fuzzy ideal in semigroups with prove. Moreover, we investigate necessary and sufficient conditions of coincidences spherical interval valued fuzzy ideals in semigroups.

On Interval Valued fuzzy Bi-Quasi Ideals in Semigroups

On Interval Valued fuzzy Bi-Quasi Ideals in Semigroups

Retracted: (m, n)-Ideals in Semigroups Based on Int-Soft Sets

Retracted: (m, n)-Ideals in Semigroups Based on Int-Soft Sets

Arf numerical semigroups with high multiplicity via Gröbner basis

ABSTRACT In this paper, Arf numerical semigroups with high multiplicity are given. RF (Row Factorization)-matrices, Gröbner basis are presented by writing the ideals of numerical semigroup with RF-matrices. In addition, it is prove that if we have a minimal presentation (or a Gröbner basis of the ideal associated to the semigroup), then this will be a system of generators of the numerical semigroup.