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Spring 2021 Root extension in polynomial and power series rings
Mi Hee Park
J. Commut. Algebra 13(1): 129-136 (Spring 2021). DOI: 10.1216/jca.2021.13.129

Abstract

An extension RS of commutative rings with unity is called a root extension if for each element sS, there exists a positive integer n such that snR. Unlike the integral extension, the root extension is not stable under polynomial ring extension. We characterize when the extension R[X]S[X] of polynomial rings is a root extension. Using the characterization, we can give a positive answer to the question posed by Anderson, Dumitrescu and Zafrullah (2004), i.e., R[X]S[X] being a root extension implies that R[X,Y]S[X,Y] is a root extension. We also characterize when the extension R[[X]]S[[X]] of power series rings is a root extension.

Citation

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Mi Hee Park. "Root extension in polynomial and power series rings." J. Commut. Algebra 13 (1) 129 - 136, Spring 2021. https://doi.org/10.1216/jca.2021.13.129

Information

Received: 5 January 2018; Revised: 24 May 2018; Accepted: 18 June 2018; Published: Spring 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.1216/jca.2021.13.129

Subjects:
Primary: 13B21, 13B25
Secondary: 13A05, 13A15, 13F25

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 1 • Spring 2021
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