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Envelope Dimension of Modules and the Simplified Radical Formula |
11 pages
Published:2012-09-21
- A. Azizi,
- A. Nikseresht,
Abstract
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 $R^{(\mathbb{N})}$. Also we 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: | envelope dimension, simplified radical formula, prime submodule |
| MSC Classifications: |
13A99 - None of the above, but in this section 13C99 - None of the above, but in this section 13C13 - Other special types 13E05 - Noetherian rings and modules |