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2019 Pullback diagrams and Kronecker function rings
Lokendra Paudel, Simplice Tchamna
Rocky Mountain J. Math. 49(7): 2267-2279 (2019). DOI: 10.1216/RMJ-2019-49-7-2267

Abstract

Knebusch and Kaiser introduced the notion of Kronecker function ring of a ring extension with respect to a star operation to generalize the classical notion of Kronecker function ring. Let $\star $ be a star operation on the extension $R\subseteq S$. Let $Kr ( \star)$ be the set of all quotients ${f}/{g}\in S(X)$ such that $f, g\in S[X]$, $c_{S}(g) = S$ and $(c_{R}(f)H)^{\star } \subseteq (c_{R}(g)H)^{\star }$ for some finitely generated $S$-regular $R$-submodule $H$ of $S$, where for each ring $A$ such that $R\subseteq A \subseteq S$, $c_{A}(g)$ denotes the content of $g\in S[X]$. The ring $Kr (\star )$ is a Kronecker subring of $S(X)$ by a theorem of Knebusch and Kaiser. We study properties of the ring $Kr (\star )$ in pullback diagrams.

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Lokendra Paudel. Simplice Tchamna. "Pullback diagrams and Kronecker function rings." Rocky Mountain J. Math. 49 (7) 2267 - 2279, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2267

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152864
MathSciNet: MR4039969
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2267

Subjects:
Primary: 13A15, 13A18, 13B02

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 7 • 2019
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