Journal article
*-Almost super-homogeneous ideals in *-h-local domains
Journal of Algebra and its Applications, Vol.21(7), 2250136
2021
DOI: 10.1142/S0219498822501365
Abstract
In this paper, we introduce *-almost independent rings of Krull type (*-almost IRKTs) and *-almost generalized Krull domains (*-almost GKDs) in the general theory of almost factoriality, neither of which need be integrally closed. This fills a gap left in [D. D. Anderson and M. Zafrullah, On *-Semi-Homogeneous Integral Domains, Advances in Commutative Algebra (Springer, Singapore, 2019)]. We characterize them by *-almost super-SH domains, where a domain D is called a *-almost super-SH domain if every nonzero proper principal ideal of D is a *-product of *-almost super-homogeneous ideals. We prove that (1) a domain D is a *-almost IRKT if and only if D is a *-almost super-SH domain, (2) a domain is a *-almost GKD if and only if D is a type 1 *-almost super-SH domain and (3) a domain D is a *-almost IRKT and an AGCD-domain if and only if D is a *-afg-SH domain. Further, we characterize them by their integral closures. For example, we prove that a domain D is an almost IRKT if and only if D ⊆ D is a root extension with D t-linked under D and D is an IRKT. Examples are given to illustrate the new concepts. © World Scientific Publishing Company.
Details
- Title: Subtitle
- *-Almost super-homogeneous ideals in *-h-local domains
- Creators
- S. Xing - Chengdu University of Information TechnologyD.D. Anderson - University of IowaM. Zafrullah - Idaho State University
- Resource Type
- Journal article
- Publication Details
- Journal of Algebra and its Applications, Vol.21(7), 2250136
- Publisher
- World Scientific
- DOI
- 10.1142/S0219498822501365
- ISSN
- 0219-4988
- Language
- English
- Electronic publication date
- 2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984230421702771
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