Journal article
Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements
Journal of Algebra, Vol.148(1), pp.17-41
1992
DOI: 10.1016/0021-8693(92)90234-D
Abstract
We define an integral domain R to be a Cohen-Kaplansky domain (CK domain) if every element of R is a finite product of irreducible elements and R has only finitely many nonassociate irreducible elements. The purpose of this paper is to investigate CK domains. Many conditions equivalent to R being a CK domain are given, for example, R is a CK domain if and only if R is a one-dimensional semi-local domain and for each nonprincipal maximal ideal M of R, R M is finite and R M is analytically irreducible, or, if and only if G ( R ), the group of divisibility of R , is finitely generated and rank G(R)= ¦ Max (R)¦ . We show that a CK domain is a certain special type of composite or pullback of a subring of a finite homomorphic image of a semilocal PID. Noetherian domains with G ( R ) finitely generated are also investigated.
Details
- Title: Subtitle
- Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements
- Creators
- D D AndersonJ L Mott
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra, Vol.148(1), pp.17-41
- DOI
- 10.1016/0021-8693(92)90234-D
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Language
- English
- Date published
- 1992
- Academic Unit
- Mathematics
- Record Identifier
- 9983986099302771
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