Book chapter
On ⋆ -Semi-homogeneous Integral Domains
Advances in Commutative Algebra, pp.7-31
Trends in Mathematics, Springer Singapore
04/12/2019
DOI: 10.1007/978-981-13-7028-1_2
Abstract
Let ⋆ be a finite character star-operation defined on an integral domain D. A nonzero finitely generated ideal of D is ⋆-homogeneous if it is contained in a unique maximal ⋆-ideal. And D is called a ⋆-semi-homogeneous (⋆-SH) domain if every proper nonzero principal ideal of D is a ⋆-product of ⋆-homogeneous ideals. Then D is a ⋆-semi-homogeneous domain if and only if the intersection D = ⋂DPP∈⋆-Max(D) is independent and locally finite where ⋆-Max(D) is the set of maximal ⋆-ideals of D. The ⋆-SH domains include h-local domains, weakly Krull domains, Krull domains, generalized Krull domains, and independent rings of Krull type. We show that by modifying the definition of a ⋆-homogeneous ideal we get a theory of each of these special cases of ⋆-SH domains.
Details
- Title: Subtitle
- On ⋆ -Semi-homogeneous Integral Domains
- Creators
- D. D Anderson - University of Iowa, MathematicsMuhammad Zafrullah - Department of Mathematics, Idaho State University, Pocatello, USA
- Resource Type
- Book chapter
- Publication Details
- Advances in Commutative Algebra, pp.7-31
- Series
- Trends in Mathematics
- DOI
- 10.1007/978-981-13-7028-1_2
- eISSN
- 2297-024X
- ISSN
- 2297-0215
- Publisher
- Springer Singapore; Singapore
- Language
- English
- Date published
- 04/12/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984231759902771
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