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Spring 2003 Some Results on $n$-Stable Rings
Amir M. Rahimi
Missouri J. Math. Sci. 15(2): 129-139 (Spring 2003). DOI: 10.35834/2003/1502129

Abstract

All rings are commutative rings with identity, and $J(R)$ denotes the Jacobson radical of the ring $R$. For any fixed integer $n\geq 1$, it is shown that the class of all $n$-stable rings is properly contained in the class of all $n+1$-stable rings. Results are given showing the connection between several types of rings whose finite sequences satisfy different stability conditions, some involving $J(R)$. It is shown that in the strongly $n$-stable case, it suffices to check whether the $n+1$-tuples satisfy the stable condition. In addition to other results and an example of a ring which is not $n$-stable for any integer $n\geq 1$, examples are given to show the distinction between the different types of stability cases. Finally, in the last section, some surjective mapping properties of a generalized form of $GL_{n}(R)$ and $SL_{n}(R)$ in connection to some stable conditions in the ring $R$ are investigated.

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Amir M. Rahimi. "Some Results on $n$-Stable Rings." Missouri J. Math. Sci. 15 (2) 129 - 139, Spring 2003. https://doi.org/10.35834/2003/1502129

Information

Published: Spring 2003
First available in Project Euclid: 31 August 2019

zbMATH: 1093.13001
MathSciNet: MR1984278
Digital Object Identifier: 10.35834/2003/1502129

Rights: Copyright © 2003 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.15 • No. 2 • Spring 2003
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