Journal article
Splitting sets in integral domains
Proceedings of the American Mathematical Society, Vol.129(8), pp.2209-2217
2001
DOI: 10.1090/S0002-9939-00-05863-9
Abstract
Let D be an integral domain. A saturated multiplicatively closed subset S of D is a splitting set if each nonzero d E D may be written as d = sa where s E S and s'D n aD = s'aD for all s' E S. We show that if S is a splitting set in D, then SU(DN) is a splitting set in DN, N a multiplicatively closed subset of D, and that S C D is a splitting set in D[X] 4==> S is an lcm splitting set of D, i.e., S is a splitting set of D with the further property that sD n dD is principal for all s E S and d E D. Several new characterizations and applications of splitting sets are given.
Details
- Title: Subtitle
- Splitting sets in integral domains
- Creators
- D. D AndersonMuhammad Zafrullah
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.129(8), pp.2209-2217
- DOI
- 10.1090/S0002-9939-00-05863-9
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Language
- English
- Date published
- 2001
- Academic Unit
- Mathematics
- Record Identifier
- 9983985857602771
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