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Transactions of the American Mathematical Society

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An embedding theorem for matrices of commutative cancellative semigroups


Author: James Streilein
Journal: Trans. Amer. Math. Soc. 208 (1975), 127-140
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1975-0374306-9
MathSciNet review: 0374306
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Abstract: In this paper it is shown that each semigroup which is a matrix of commutative cancellative semigroups has a ``quotient semigroup'' which is a completely simple semigroup with abelian maximal subgroups. This result is proved by explicitly constructing the quotient semigroup. The paper also gives necessary and sufficient conditions for a semigroup of the type being considered in the paper to be isomorphic to a Rees matrix semigroup over a commutative cancellative semigroup. Several special cases and examples are also briefly discussed.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0374306-9
Keywords: Matrix of commutative cancellative semigroups, Rees matrix semigroup, quotient Rees matrix semigroup, quotient group
Article copyright: © Copyright 1975 American Mathematical Society