ℋ-commutative semigroups in which each homomorphism is uniquely determined by its kernel

Tully, Edward J.

doi:10.2140/pjm.1973.45.669

Cited by 4 publications

(5 citation statements)

References 5 publications

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“…In this direction, a very recent significant and remarkable work have been made by Ahanger and Shah on partially ordered semigroups (posemigroups), and commutative posemigroups (see [1][2][3], [23]). Now, we begin with the class of H-commutative semigroups whose concept was first developed by Tully [25]. In [19], Nagy presented a new concept of H-commutativity, i.e., for all a, b ∈ S, there exists x ∈ S 1 such that ab � bxa.…”

Section: Preliminariesmentioning

confidence: 99%

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Alam

Khan

Obeidat

et al. 2022

Journal of Mathematics

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In this paper, we discussed some saturated classes of ℋ -commutative semigroups, left (right) regular semigroups, medial semigroups, and paramedial semigroups. The results of this paper significantly extend the long standing result about normal bands that normal bands were saturated and, thus, significantly broaden the class of saturated semigroups.

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Section: Preliminariesmentioning

confidence: 99%

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Alam

Khan

Obeidat

et al. 2022

Journal of Mathematics

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“…Some of the results of the paper also apply to non-regular semigroups, and we try to avoid regularity assumption when it is not necessary. Since we can consider group invertible elements as idempotents modulo H, we consider here semigroups whose group invertible elements H-commute (commutation modulo H was introduced by Tully [20]). Lemma 3.1.…”

Section: Completely Inverse Semigroups and H-orthodox Semigroupsmentioning

confidence: 99%

Classes of semigroups modulo Green’s relation $\mathcal{H}$

Mary

2013

Semigroup Forum

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Inverses semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green's relation H, or in terms of the set of group invertible elements H(S), that allows a study of non-regular semigroups. We then study the interplays between these new classes of semigroups, as well as with known classes of semigroups (notably inverse, orthodox and cryptic semigroups). * We will make use of the Green's preorders and relations in a semigroup [5]. For elements a and b of S, Green's preorders ≤ L , ≤ R and ≤ H are defined by a ≤ L b ⇐⇒ S 1 a ⊂ S 1 b ⇐⇒ ∃x ∈ S 1 , a = xb; a ≤ R b ⇐⇒ aS 1 ⊂ bS 1 ⇐⇒ ∃x ∈ S 1 , a = bx;

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“…In this article, we are concerned with a series of results and examples that explore the class of semigroups S for which Green's relation H is commutative: abHba for all a, b in S. This definition of H-commutativity was introduced by Tully in [13]. In ( [11], We now introduce dominions of semigroups.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The class of H-commutative semigroups had been studied by several authors in one way or the other (see [9], [10], [11], [12] and [13] for example). The class of Hcommutative semigroups was first investigated by Tully [13]. He studied H-commutative semigroups with the additional property that each congruence is uniquely determined by its kernel relative to a given element g and claimed that H-commutative semigroups were precisely those semigroups with Green's relation H a commutative congruence.…”

Section: Introductionmentioning

confidence: 99%

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Epimorphisms, dominions and $$\mathcal {H}$$-commutative semigroups

2019

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In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalize a result of Isbell from commutative semigroups to H-commutative semigroups by showing that the dominion of an H-commutative semigroup is H-commutative. We then use this to generalize Howie and Isbell's result that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated.

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ℋ-commutative semigroups in which each homomorphism is uniquely determined by its kernel

Cited by 4 publications

References 5 publications

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Classes of semigroups modulo Green’s relation $\mathcal{H}$

Epimorphisms, dominions and $$\mathcal {H}$$-commutative semigroups

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