Journal article
General ZPI-rings without identity
Houston Journal of Mathematics, Vol.33(3), pp.631-634
2007
Abstract
Let R be a commutative ring not necessarily having an identity. Then R is a general ZPI-ring if every ideal of R is a product of prime ideals. S. Mori showed that a general ZPI-ring without identity is either (1) an integral domain, (2) a ring R where every ideal of R including O is a power of R, (3) K × R where AT is a field and R is a ring as in (2), or (4) K × D where K is a field and D is a domain with every nonzero ideal of D a power of D. The purpose of this paper is to prove that if A is a ring as in (2), then there is an SPIR S with S = R[π] having R as its maximal ideal. Moreover, there is a complete DVR (D, (π)) with D = (π)[1] SO that S and R are homomorphic images of D and (π), respectively. © 2007 University of Houston.
Details
- Title: Subtitle
- General ZPI-rings without identity
- Creators
- D.D. AndersonJ.S. Kintzinger
- Resource Type
- Journal article
- Publication Details
- Houston Journal of Mathematics, Vol.33(3), pp.631-634
- ISSN
- 0362-1588
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9984230627802771
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