Korean Journal of Mathematics

  • 제30권2호
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  • Pages.283-296
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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IDENTITIES PRESERVED UNDER EPIS OF PERMUTATIVE POSEMIGROUPS

  • 투고 : 2021.09.30
  • 심사 : 2022.06.01
  • 발행 : 2022.06.30
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⟨ 이전 논문 다음 논문 ⟩

초록

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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참고문헌

  1. Ahanger, S. A., Shah, A. H., Epis, Dominions and Varieties of Commutative Posemigroups, Asian-Eur. J. Math., 14 (4) (2021), 2150048. https://doi.org/10.1142/S1793557121500480
  2. Ahanger, S. A., Shah, A. H., Khan, N. M., On Saturated Varieties of Permutative Posemigroups, Algebra Univers., 81 (48) (2020), 1-11. https://doi.org/10.1007/s00012-019-0630-4
  3. Ahanger, S. A., Shah, A. H., Bano, S., Epis and Varieties of Posemigroups, submitted (2020).
  4. Ahanger, S. A., Shah, A. H., Khan, N. M., Permutative Varieties of Posemigroups, Commun. Algebra, 49 (7) (2021), 2758-2774. https://doi.org/10.1080/00927872.2021.1882474
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  6. Howie, J. M., Fundamentals of Semigroup Theory, Clarendon Press, Oxford (1995).
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  8. N. M. Khan, Epimorphically Closed Permutative Varieties, Trans. Amer. Math. Soc., 287 (2) (1985), 507-528. https://doi.org/10.1090/S0002-9947-1985-0768723-9
  9. Sohail, N., Tart, L., Dominions, Zigzags and Epimorphism for partially ordered semigroups, Acta Commen. Univ. Tartu. Math., 18 (1) (2014), 81-91. https://doi.org/10.12697/ACUTM.2014.18.09