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Envelope Dimension of Modules and the Simplified Radical Formula
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- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 4 / 01 December 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 683-694
- Print publication:
- 01 December 2013
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- Article
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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.
