Journal article
Finitely Generated Multiplicative Subsemigroups of Rings
Semigroup forum, Vol.55(3), pp.294-298
11/1997
DOI: 10.1007/PL00005930
Abstract
Isbell showed that if R is a commutative ring (not necessarily with identity) with multiplicative semigroup (R, .) finitely generated, then R is actually finite. Let Z(R) and U(R) denote the zero divisors and units of R, respectively. We show that the multiplicative subsemigroup (Z(R), .) of (R, .) (respectively, (R -U(R), .)) is finitely generated if and only if R is finite or R is an integral domain (respectively, a field).
Details
- Title: Subtitle
- Finitely Generated Multiplicative Subsemigroups of Rings
- Creators
- D.D Anderson
- Resource Type
- Journal article
- Publication Details
- Semigroup forum, Vol.55(3), pp.294-298
- DOI
- 10.1007/PL00005930
- ISSN
- 0037-1912
- eISSN
- 1432-2137
- Language
- English
- Date published
- 11/1997
- Academic Unit
- Mathematics
- Record Identifier
- 9983985838302771
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