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Some Semigroups Having Quasi-Frobenius Algebras. II

Published online by Cambridge University Press:  20 November 2018

R. Wenger
R. Wenger*
Affiliation:
University of Delaware, Newark, Delaware
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The investigation of finite semigroups S with quasi-Frobenius (q.-F.) algebras F(S) over a field F was begun in (7; 8). The problem for commutative semigroups was reduced (7, Theorem 3) to the study of semigroups of the form S = G ∪ S1, where G is a group and S1 is either the null set or is a nilpotent ideal in S (i.e., S1n = {0} for some positive integer n). Such semigroups were called “of type C”. The question is “When does a semigroup of type C have a q.-F. algebra over a field?” (7, Theorem 4) shows that no distinction need be made between the properties q.-F. and Frobenius for commutative algebras.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 615 - 624
Copyright
Copyright © Canadian Mathematical Society 1969

References

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