1. Two applications of Nagata rings and modules.
- Author
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Wang, Fanggui and Qiao, Lei
- Subjects
- *
TORSION theory (Algebra) , *CATEGORIES (Mathematics) , *APPLIED mathematics , *COMMUTATIVE rings , *MATHEMATICS - Abstract
Let τ be a finite type hereditary torsion theory on the category of all modules over a commutative ring. The purpose of this paper is to give two applications of Nagata rings and modules in the sense of Jara [Nagata rings, Front. Math. China10 (2015) 91–110]. First they are used to obtain Chase's Theorem for τ -coherent rings. In particular, we obtain the w -version of Chase's Theorem, where w is the classical star operation in ideal theory. In the second half, we apply they to characterize τ -flatness in the sense of Van Oystaeyen and Verschoren [Relative Invariants of Rings-The Commutative Theory, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 79 (Marcel Dekker, Inc., New York, 1983)]. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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