Journal article
Commutative Rings with Finitely Generated Multiplicative Semigroup
SemiGroup Forum, Vol.60(3), pp.436-443
05/2000
DOI: 10.1007/s002339910035
Abstract
be a commutative ring not necessarily with identity. J.R. Isbell showed that if (R, ·) is finitely generated, then R is actually finite. We give a simple ring-theoretic proof of this result. We show that (R, ·) is a subsemigroup of a cyclic semigroup if and only if R is finite with R 2=0, but that any countable ring R with R 2=0 has (R,·) as a subsemigroup of a doubly generated semigroup. We also characterize the commutative rings R with (R, ·) generated by two or fewer elements.
Details
- Title: Subtitle
- Commutative Rings with Finitely Generated Multiplicative Semigroup
- Creators
- D.D AndersonJ Stickles
- Resource Type
- Journal article
- Publication Details
- SemiGroup Forum, Vol.60(3), pp.436-443
- Publisher
- Springer-Verlag; New York
- DOI
- 10.1007/s002339910035
- ISSN
- 0037-1912
- eISSN
- 1432-2137
- Language
- English
- Date published
- 05/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9983986097502771
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