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<p>In this paper we introduce lower convex [upper convex] and convex posemigroups and using these notions we characterize saturated permutative varieties of posemigroups. Our results extend the characterization of N. M. Khan [J. Aust. Math. Soc. (Ser. A) 38, 186–197 (1985)] in the category of posemigroups. Further, N. M. Khan [Bull. Aust. Math. Soc. 38, 419–425 (1983)], provided sufficient conditions for homotypical and heterotypical varieties of semigroups, respectively, to be saturated. We prove that these are also the sufficient conditions for such varieties to be saturated in the category of posemigroups if they are convex. We exhibit examples to illustrate that by dropping convexity any such variety is not saturated.</p>

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Epimorphisms and convex varieties of posemigroups

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Shabir Ahmad Ahanger,
  • Aftab Hussain Shah,
  • Sakeena Bano,
  • Noor Alam

摘要

In this paper we introduce lower convex [upper convex] and convex posemigroups and using these notions we characterize saturated permutative varieties of posemigroups. Our results extend the characterization of N. M. Khan [J. Aust. Math. Soc. (Ser. A) 38, 186–197 (1985)] in the category of posemigroups. Further, N. M. Khan [Bull. Aust. Math. Soc. 38, 419–425 (1983)], provided sufficient conditions for homotypical and heterotypical varieties of semigroups, respectively, to be saturated. We prove that these are also the sufficient conditions for such varieties to be saturated in the category of posemigroups if they are convex. We exhibit examples to illustrate that by dropping convexity any such variety is not saturated.