Varieties of commutative semigroups

Kisielewicz, Andrzej

doi:10.1090/S0002-9947-1994-1211411-0

Varieties of commutative semigroups
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by Andrzej Kisielewicz

Trans. Amer. Math. Soc. 342 (1994), 275-306

DOI: https://doi.org/10.1090/S0002-9947-1994-1211411-0

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Abstract:

In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform solution to the word problems for free objects in all varieties of commutative semigroups.

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Semigroup varieties with modular subvariety lattices