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http://dx.doi.org/10.11568/kjm.2022.30.2.283

IDENTITIES PRESERVED UNDER EPIS OF PERMUTATIVE POSEMIGROUPS  

Shah, Aftab Hussain (Department of Mathematics, Central University of Kashmir)
Bano, Sakeena (Department of Mathematics, Central University of Kashmir)
Ahanger, Shabir Ahmad (Department of Mathematics, Central University of Kashmir)
Publication Information
Korean Journal of Mathematics / v.30, no.2, 2022 , pp. 283-296 More about this Journal
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.
Keywords
Posemigroups; Dominion; Zigzag; Identity;
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  • Reference
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