On uniform acts over semigroups

Roueentan, Mohammad; Sedaghatjoo, Mojtaba

doi:10.1007/s00233-017-9908-z

Cited by 9 publications

(13 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that in [9,Corollary 3.21], it is proved that for any subdirectly irreducible act A with two zero elements over a semigroup S, |A| ≤ 2 |S|+1 . Therefore, Proposition 3.5 sharpens this bound.…”

Section: Proofmentioning

confidence: 99%

“…Analogous arguments and terminologies can be employed for semigroups as right acts over themselves. For a thorough account on the preliminaries, the reader is referred to [2,3,9].…”

Section: Introductionmentioning

confidence: 99%

“…Thereby, in light of determining any variety of algebras of the same type by its subdirectly irreducible members (Birkhoff's theorem), the class of subdirectly irreducible acts, was a matter of interest in literatures and was followed by some authors for instance Kozhukhov in [4,5,6,7]. Uniform acts that are generalizations of subdirectly irreducible acts, were investigated in a specific case in [1] by Feller and Gantos as a pioneering work whilst the recent work [9], presents a general account on this issue.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The structure of subdirectly irreducible and uniform acts over rectangular bands

Sedaghatjoo

Roueentan²

2020

Semigroup Forum

Self Cite

View full text Add to dashboard Cite

The aim of this paper is characterizing right subdirectly irreducible completely 0-simple semigroups. We prove that such semigroups are indeed groups with least nontrivial subgroups. On the other hand we prove that right irreducible completely 0-simple semigroups are groups for which nontrivial subgroups have nontrivial intersection. Ultimately, we characterize the class of uniform acts as an overclass of subdirectly irreducible acts over rectangular bands.2010 Mathematics Subject Classification. 20M20, 20M30. Key words and phrases. completely 0-simple semigroup, rectangular band, right congruence, right subdirectly irreducible semigroup, uniform act.Definition 2.1. For a semigroup S, an S-act A is called unif orm if every nonzero subact is large in A. Also a semigroup S is called right (left) uniform if the right (left) S-act S S ( S S) is uniform.Definition 2.2. A subset B of a right S-act A is called separated, provided that for a = b ∈ B there exists s ∈ S\{1} such that as = bs.The next two results, stated below, are preliminary results of uniform acts needed in the next argument.Corollary 2.3. [9, Corollary 3.15] If S is a right uniform semigroup and xy = y for x, y ∈ S, then x is a left identity or y is a left zero.

show abstract

Section: Proofmentioning

confidence: 99%

“…Analogous arguments and terminologies can be employed for semigroups as right acts over themselves. For a thorough account on the preliminaries, the reader is referred to [2,3,9].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The structure of subdirectly irreducible and uniform acts over rectangular bands

Sedaghatjoo

Roueentan²

2020

Semigroup Forum

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, the descending and ascending chain conditions on commutative monoids with zero elements as S-acts have been discussed. As defined in [13], an S-act is called noetherian (respectively, strongly noetherian) if it satisfies the ascending chain condition for subacts (respectively, congruences).…”

Section: Introductionmentioning

confidence: 99%

Chain conditions on (Rees) congruences of S-acts

Khosravi¹,

Roueentan²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce (Rees) artinian S-acts as those acts that satisfy the descending chain condition on their (Rees) congruences. Then, we show that artinian S-acts are those acts whose all factor acts are finitely (Rees) cogenerated. In addition, we continue the study of (Rees) noetherian S-acts, namely, those acts whose (Rees) congruences are finitely generated. Moreover, as a useful tool for the investigation of chain conditions, we prove that the properties of being (Rees) noetherian and artinian are inherited in Rees short exact sequences. Next, we specifically consider the chain conditions on monoids. Finally, we prove that every right Rees artinian, commutative monoid is right Rees noetherian.

show abstract

“…In Section 2, We consider the properties of coessential and superfluous subacts. In [9], the authors investigated uniform acts over a semigroup S, as S-acts that all their non-zero subacts are large. In module theory, the dual notion of a uniform module is that of a hollow module.…”

Section: Introductionmentioning

confidence: 99%

Co-uniform and hollow S-acts over monoids

Khosravi,

Roueentan

2019

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we first introduce the notions of superfluous and coessential subacts. Then hollow and co-uniform S-acts are defined as the acts that all proper subacts are superfluous and coessential, respectively. Also it is indicated that the class of hollow S-acts is properly between two classes of indecomposable and locally cyclic S-acts. Moreover, using the notion of radical of an S-act as the intersection of all maximal subact, the relations between hollow and local S-acts are investigated. Ultimately, the notion of a supplement of a subact is defined to characterize the union of hollow S-act.

show abstract

On uniform acts over semigroups

Cited by 9 publications

References 11 publications

The structure of subdirectly irreducible and uniform acts over rectangular bands

The structure of subdirectly irreducible and uniform acts over rectangular bands

Chain conditions on (Rees) congruences of S-acts

Co-uniform and hollow S-acts over monoids

Contact Info

Product

Resources

About