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For a finite ring $R$, not necessarily commutative, we prove that the category of $text{VIC}(R)$-modules over a left Noetherian ring $mathbf{k}$ is locally Noetherian, generalizing a theorem of the authors that dealt with commutative $R$. As an application, we prove a very general twisted homology stability for $text{GL}_n(R)$ with $R$ a finite noncommutative ring.
A commutative ring R has finite rank r, if each ideal of R is generated at most by r elements. A commutative ring R has the r-generator property, if each finitely generated ideal of R can be generated by r elements. Such rings are closely related to
Let $n>1$ be an integer, $alphain{mathbb C}^n$, $bin{mathbb C}$, and $V$ a $mathfrak{gl}_n$-module. We define a class of weight modules $F^alpha_{b}(V)$ over $sl_{n+1}$ using the restriction of modules of tensor fields over the Lie algebra of vector
Let $dge1$ be an integer, $W_d$ and $mathcal{K}_d$ be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=mathbb{C} [x_1^{pm1}, x_2^{pm1}, ..., x_d^{pm1}]$, respectively. For any $mathfrak{gl}_d$-module $M$ and any admissib
For an irreducible module $P$ over the Weyl algebra $mathcal{K}_n^+$ (resp. $mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $mathfrak{gl}_n$, using Shens monomorphism, we make $Potimes M$ into a module over the Witt a
Let $k$ be an algebraically closed field, let $A$ be a finite dimensional $k$-algebra and let $V$ be a $A$-module with stable endomorphism ring isomorphic to $k$. If $A$ is self-injective then $V$ has a universal deformation ring $R(A,V)$, which is a