Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new Homological Invariant for Modules   Let $R$ be a commutative Noetherian local ring with residue field $k$. Using
the structure of Vogel cohomology, for any finitely generated module $M$, we
introduce a new dimension, called $\zeta$-dimension, denoted by $\zeta-dim_R
M$. This dimension is finer than Gorenstein dimension and has nice properties
enjoyed by homological dimensions. In particular, it characterizes Gorenstein
rings in the sense that: a ring $R$ is Gorenstein if and only if every finitely
generated $R$-module has finite $\zeta$-dimension. Our definition of
$\zeta$-dimension offer a new homological perspective on the projective
dimension, complete intersection dimension of Avramov et al. and $G$-dimension
of Auslander and Bridger.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex