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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 rings
Categories: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 rings
Categories: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

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