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Polynomial extensions of semistar operations
- Authors
- Chang, Gyu Whan; Fontana, Marco; Park, Mi Hee
- Issue Date
- Sep-2013
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Semistar operation; Finite type; Stable; Strict extension; d-, b-, v-, t-, w-operation
- Citation
- JOURNAL OF ALGEBRA, v.390, pp 250 - 263
- Pages
- 14
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 390
- Start Page
- 250
- End Page
- 263
- ISSN
- 0021-8693
1090-266X
- Abstract
- We provide a complete solution to the problem of extending arbitrary semistar operations of an integral domain D to semistar operations of the polynomial ring D[X]. As an application, we show that one can reobtain the main results of the papers in Chang and Fontana (2007, 2011) [1,2] concerning the problem in the special cases of stable semistar operations of finite type or semistar operations defined by families of overrings. Finally, we investigate the behavior of the polynomial extensions of the most important and classical operations such as d(D), v(D), t(D), w(D) and b(D) operations. (C) 2013 Elsevier Inc. All rights reserved.
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