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Winter 2002 An Application of $SB$-Rings
Amir M. Rahimi
Missouri J. Math. Sci. 14(1): 57-58 (Winter 2002). DOI: 10.35834/2002/1401057

Abstract

All rings are commutative rings with identity and $J(R)$ denotes the Jacobson radical of a ring $R$. A ring $R$ is called a $SB$-ring provided that for any sequence $a_1, a_2, \ldots , a_s, a_{s+1}$ of elements in $R$ with $s \ge 2$ and $(a_1, a_2, \ldots , a_{s-1} ) \not\subseteq J(R)$, there exists $b \in R$ such that $(a_1, a_2, \ldots a_s, a_{s+1}) = (a_1, a_2, \ldots , a_s + ba_{s+1})$. By applying some of the properties of $SB$-rings, it is shown that $R[X]$ is not a Prüfer domain for any Noetherian domain $R$ which is not a field.

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Amir M. Rahimi. "An Application of $SB$-Rings." Missouri J. Math. Sci. 14 (1) 57 - 58, Winter 2002. https://doi.org/10.35834/2002/1401057

Information

Published: Winter 2002
First available in Project Euclid: 4 October 2019

zbMATH: 1051.13009
MathSciNet: MR1884011
Digital Object Identifier: 10.35834/2002/1401057

Rights: Copyright © 2002 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.14 • No. 1 • Winter 2002
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