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Results tagged with ac.commutative-algebra
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user 38807
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Example of indecomposable self injective ring
If $R$ is noetherian, then $R$ is gorenstein of dimension zero, hence artinian. In particular, $R$ is a finite direct product of local artinian rings. If you mean $R$ is indecomposable as a direct p …
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Computation of Quillen K-groups for mod R
The recent paper K-Groups for Rings of Finite Cohen-Macaulay Type by H. Holm allows us to compute the Quillen $K$-group $K_1(\text{mod}\hspace{.1 cm}R)$ as a quotient of the abelianization of the auto …
4
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Centers of Noetherian Algebras and K-theory
I'll start off a little vauge: Let $E$ be a noncommutative ring which is finitely generated over its noetherian center $Z$. Denote by $\textbf{mod}\hspace{.1 cm} E$ the category of finitely generate …
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3
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269
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Computing the Abelianization of an Automorphism Group
Setup: We are working in a Henselian local ring $(R, \mathfrak m, k)$ that way may assume is Cohen-Macaulay, admits a canonical module and is of finite type (so is an isolated singularity). Let $M_1 …
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3
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Endomorphism Ring of Indecomposable MCM Modules
Let $R = k[[x, y]]/(f)$, where $k$ is algebraically closed of characteristic zero. I'm particularly interested in studying the endomorphism ring of indecomposable MCM (maximal Cohen-Macaulay) modules …
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