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

Alam, Noor; Higgins, Peter M.; Khan, Noor Mohammad

doi:10.1007/s00233-019-10050-z

Cited by 6 publications

(3 citation statements)

References 11 publications

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“…Moreover, Shah et al [9] have shown that classes of structurally (n, m)-generalized inverse semigroups are saturated as well. Furthermore, Alam et al [10] have extended Howie's and Isbell's result to show that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated. In a related direction, Ahanger et al [11] have established the saturation of generalized left [right] regular semigroups.…”

Section: Theorem 5 ([6] (Theorem 54))mentioning

confidence: 99%

Saturated Varieties of Semigroups

Nabi,

Alali,

Bano

2023

Symmetry

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The complete characterization of saturated varieties of semigroups remains an unsolved problem. The primary objective of this paper is to make significant progress in this direction. We initially demonstrate that the variety of semigroups defined by the identity axy=ayxa is saturated. The next main result establishes that the variety of semigroups determined by the identity axy=ayax is saturated. Finally, we show that medial semigroups satisfying the identity xy=xyn, where n≥2, are also saturated. These results collectively lead to the conclusion that epis from these saturated varieties are onto. This paper thus offers substantial progress towards the comprehensive characterization of saturated varieties of semigroups.

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Section: Theorem 5 ([6] (Theorem 54))mentioning

confidence: 99%

Saturated Varieties of Semigroups

Nabi,

Alali,

Bano

2023

Symmetry

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“…1,18). Recently, the structure of semigroups of this class has been explored by Alam, Higgins, and Khan [5].…”

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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“…In [4], Alam and Khan have shown that the variety of semigroups satisfying the identity x y = x yx [yx = x yx] is closed. Next we generalize this result by showing that for each n ≥ 2 ∈ N, the variety of semigroups satisfying the identity…”

Section: Lemma 28 For All Kmentioning

confidence: 99%

Some homotypical closed varieties of semigroups

et al. 2022

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We show that for each $$n\ge 2\in {\mathbb {N}}$$ n ≥ 2 ∈ N , the varieties $${\mathbb {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$ V n = [ x 1 x 2 x 3 = x 1 n x i 1 x i 2 x i 3 ] where i is any non-trivial permutation of $$\{1,2,3\}$$ { 1 , 2 , 3 } are closed. Further, we show that for each $$n\in {\mathbb {N}}$$ n ∈ N , the varieties $${\mathcal {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$ V n = [ x 1 x 2 x 3 = x 1 n x i 1 x i 2 x i 3 ] where i is any non-trivial permutation of $$\{1,2,3\}$$ { 1 , 2 , 3 } other than the permutation (231) are closed.

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

Cited by 6 publications

References 11 publications

Saturated Varieties of Semigroups

Saturated Varieties of Semigroups

Epimorphisms, Dominions, and Various Classes of Saturated Semigroups

Some homotypical closed varieties of semigroups

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