On closedness of some permutative posemigroup identities

Document Type : Research Paper

Authors

Department of Mathematics, Aligarh Muslim University, Aligarh, India

Abstract

As we know that all non-trivial permutation identities  are not preserved under epimorphisms of partially ordered semigroups.  In this paper towards this open problem, first we show that certain non-trivial identities in conjunction with the permutation identity z1z2⋯zn=zi1zi2⋯zin (n≥2) with in≠n  [i1≠1]  are preserved under epimorphisms of partially ordered semigroups. Further, we extend a result of Ahanger and Shah which showed that the center of a partially ordered semigroup S is closed in S and show that the normalizer of any element of a partially ordered semigroup S is closed in S.

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References

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Journal of Algebra and Related Topics
Volume 12, Issue 1
July 2024
Pages 1-12

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