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Search: MSC category 16E65 ( Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) )

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1. CMB Online first

Nasseh, Saeed
 On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions We show under some conditions that a Gorenstein ring \$R\$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does \$R[x]\$. When \$R\$ is a local ring we prove the same result for some localizations of \$R[x]\$. Keywords:Auslander-Reiten conjecture, finitistic extension degree, Gorenstein ringsCategories:13D07, 16E30, 16E65

2. CMB Online first

Nasseh, Saeed
 On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions We show under some conditions that a Gorenstein ring \$R\$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does \$R[x]\$. When \$R\$ is a local ring we prove the same result for some localizations of \$R[x]\$. Keywords:Auslander-Reiten conjecture, finitistic extension degree, Gorenstein ringsCategories:13D07, 16E30, 16E65

3. CMB 2004 (vol 47 pp. 445)

Pirkovskii, A. Yu.
 Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators For a locally compact group \$G\$, the convolution product on the space \$\nN(L^p(G))\$ of nuclear operators was defined by Neufang \cite{Neuf_PhD}. We study homological properties of the convolution algebra \$\nN(L^p(G))\$ and relate them to some properties of the group \$G\$, such as compactness, finiteness, discreteness, and amenability. Categories:46M10, 46H25, 43A20, 16E65