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2019 The ascending chain condition on principal ideals in composite generalized power series rings
Jung Wook Lim, Dong Yeol Oh
Rocky Mountain J. Math. 49(4): 1223-1236 (2019). DOI: 10.1216/RMJ-2019-49-4-1223

Abstract

Let $D \subseteq E$ be an extension of commutative rings with identity, $I$ a nonzero proper ideal of $D$, $(\Gamma , \leq )$ a strictly totally ordered monoid such that $0 \leq \alpha $ for all $\alpha \in \Gamma $, and $\Gamma ^*=\Gamma \setminus \{0\}$. Let $D+[\![E^{\Gamma ^*, \leq }]\!]=\{f \in [\![E^{\Gamma , \leq }]\!] \mid f(0) \in D\}$ and $D+[\![I^{\Gamma ^*, \leq }]\!] =\{f \in [\![D^{\Gamma , \leq }]\!] \mid f(\alpha ) \in I$ for all $\alpha \in \Gamma ^*\}$. In this paper, we give some conditions for the rings $D+[\![E^{\Gamma ^*, \leq }]\!]$ and $D+[\![I^{\Gamma ^*, \leq }]\!]$ to satisfy the ascending chain condition on principal ideals.

Citation

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Jung Wook Lim. Dong Yeol Oh. "The ascending chain condition on principal ideals in composite generalized power series rings." Rocky Mountain J. Math. 49 (4) 1223 - 1236, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1223

Information

Published: 2019
First available in Project Euclid: 29 August 2019

zbMATH: 07104715
MathSciNet: MR3998919
Digital Object Identifier: 10.1216/RMJ-2019-49-4-1223

Subjects:
Primary: 13A02, 13A15, 13E99, 13G05

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 4 • 2019
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