Locally pseudo-valuation domains with only finitely many star operations
- Authors
- Houston, Evan; Lee, Eun Kyung; Park, Mi Hee
- Issue Date
- Dec-2015
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Star operation; Locally pseudo-valuation domain; Prufer domain
- Citation
- JOURNAL OF ALGEBRA, v.444, pp 1 - 19
- Pages
- 19
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 444
- Start Page
- 1
- End Page
- 19
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/8813
- DOI
- 10.1016/j.jalgebra.2015.06.036
- ISSN
- 0021-8693
1090-266X
- Abstract
- Let R be a locally pseudo-valuation domain. For each maximal ideal M of R, denote by V(M) the associated valuation domain of the pseudo-valuation domain R-M, and let T = boolean AND V(M)" We characterize those R that have only finitely many star operations. When (R : T) not equal(0), the characterization becomes: R has only finitely many star operations if and only if T and each R-M have only finitely many star operations. On the other hand, if (R : T) = (0), then neither direction of this equivalence holds, and we give examples to illustrate the various possibilities. (C) 2015 Elsevier Inc. All reserved.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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