Korean J. Math. Vol. 30 No. 2 (2022) pp.283-296
DOI: https://doi.org/10.11568/kjm.2022.30.2.283

Identities preserved under epis of permutative posemigroups

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Published: Jun 30, 2022
Keywords:
Posemigroups, Dominion, Zigzag, Identity
Mathematics Subject Classification:
20Mxx, 20M10

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Aftab Hussain Shah
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India
Sakeena Bano
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India
Shabir Ahmad Ahanger
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India

Abstract

In 1985, Khan gave some sufficient conditions on semigroup identities to be preserved under epis of semigroups in conjunction with the general semigroup permutation identity. But determination of all identities which are preserved under epis in conjunction with the general permutation identity is an open problem in the category of all semigroups and hence, in the category of all posemigroups. In this paper, we first find some sufficient conditions on an identity to be preserved under epis of posemigroups in conjunction with any nontrivial general permutation identity. We also find some sufficient conditions on posemigroup identities to be preserved under epis of posemigroups in conjunction with the posemigroup permutation identity, not a general permutation identity.



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