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Semiprime semigroup rings and a problem of J. Weissglass

Published online by Cambridge University Press:  18 May 2009

Mark L. Teply
Mark L. Teply
Affiliation:
University of Florida, Gainesville, Florida 32611
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If R is a ring and S is a semigroup, the corresponding semigroup ring is denoted by R[S]. A ring is semiprime if it has no nonzero nilpotent ideals. A semigroup S is a semilattice P of semigroups Sα if there exists a homomorphism φ of S onto the semilattice P such that Sα = αφ−1 for each α ∈ P.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 131 - 134
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. I, Math. Surveys No. 7, Amer. Math. Soc. (Providence, R. I., 1961).Google Scholar
2.Petrich, M., Introduction to semigroups (Merrill, Columbus, 1973).Google Scholar
3.Teply, M. L., Turman, E. G., and Quesada, A., On semisimple semigroup rings, Proc. Amer. Math. Soc. (to appear).Google Scholar
4.Weissglass, J., Semigroup rings and semilattice sums of rings, Proc. Amer. Math. Soc. 39 (1973), 471–478.CrossRefGoogle Scholar