Geodesic
Envelope Dimension of Modules and the Simplified Radical Formula
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 683-694

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DOI

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.
DOI : 10.4153/CMB-2012-029-3
Mots-clés : 13A99, 13C99, 13C13, 13E05, envelope dimension, simplified radical formula, prime submodule 
Nikseresht, A.; Azizi, A. Envelope Dimension of Modules and the Simplified Radical Formula. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 683-694. doi: 10.4153/CMB-2012-029-3
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     title = {Envelope {Dimension} of {Modules} and the {Simplified} {Radical} {Formula}},
     journal = {Canadian mathematical bulletin},
     pages = {683--694},
     year = {2013},
     volume = {56},
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     doi = {10.4153/CMB-2012-029-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-029-3/}
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