Finite monogenic semigroups and saturated varieties of semigroups

Abstract

J. M. Howie has shown that the finite monogenic semigroups are absolutely closed. We provide a new, simple and direct proof of Howie’s result. We also show that all the varieties defined by the identities ax = axa, axy = axay and axy = axyay are saturated if and only if they are epimorphically closed.

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Correspondence to Shabir Ahmad Ahanger.

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Communicated by Marcel Jackson.

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Ahanger, S.A. Finite monogenic semigroups and saturated varieties of semigroups. Semigroup Forum (2020). https://doi.org/10.1007/s00233-020-10111-8

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Keywords

  • Dominion
  • Zigzag equations
  • Absolutely closed semigroups
  • Epimorphically closed and saturated varieties