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Varieties of commutative semigroups


Author: Andrzej Kisielewicz
Journal: Trans. Amer. Math. Soc. 342 (1994), 275-306
MSC: Primary 20M07; Secondary 03C05, 08B05, 20M05
DOI: https://doi.org/10.1090/S0002-9947-1994-1211411-0
MathSciNet review: 1211411
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1211411-0
Keywords: Commutative semigroup, variety, equational theory, lattice of varieties, identity, consequence relation
Article copyright: © Copyright 1994 American Mathematical Society

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