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Envelope Dimension of Modules and the Simplified Radical Formula

Published online by Cambridge University Press:  20 November 2018

A. Nikseresht  and
A. Azizi
A. Nikseresht
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, 71457-44776, Shiraz, Iran e-mail: a_nikseresht@shirazu.ac.iraazizi@shirazu.ac.ir
A. Azizi
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, 71457-44776, Shiraz, Iran e-mail: a_nikseresht@shirazu.ac.iraazizi@shirazu.ac.ir
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Abstract.

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We introduce and investigate the notion of envelope dimension of commutative rings and modules over them. In particular, we show that the envelope dimension of a ring, $R$, is equal to that of the $R$-module ${{\mathbb{R}}^{\left( \mathbb{N} \right)}}$. We also prove that the Krull dimension of a ring is no more than its envelope dimension and characterize Noetherian rings for which these two dimensions are equal. Moreover, we generalize and study the concept of simplified radical formula for modules, which we defined in an earlier paper.

Keywords

13A9913C9913C1313E05envelope dimensionsimplified radical formulaprime submodule
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 683 - 694
Copyright
Copyright © Canadian Mathematical Society 2013

Footnotes

The first author is partially funded by the National Elite Foundation.

References

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