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The varieties of commutative semigroups for which epis are onto

Published online by Cambridge University Press:  14 November 2011

P. M. Higgins
P. M. Higgins
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, Australia 3168
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Synopsis

In a forthcoming paper, N. M. Khan gives a condition for a variety of commutative semigroups V to be saturated in the sense of Howie and Isbell (1967) (i.e. epis are onto for each S ∈ V). We show the necessity of the condition by constructing a non-saturated semigroup which is a member of every commutative variety not satisfying Khan's condition. This determination of the saturated varieties of commutative semigroups enables us then to prove that these varieties form a sublattice of the lattice of varieties of all commutative semigroups.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 1 - 7
Copyright
Copyright © Royal Society of Edinburgh 1983

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