ﻻ يوجد ملخص باللغة العربية
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 complete local commutative Noetherian $k$-algebra with residue field $k$. Moreover, if $Lambda$ is also a Frobenius $k$-algebra then $R(A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $Ar$-modules whose stable endomorphism ring isomorphic to $k$, where $Ar$ is a symmetric special biserial $k$-algebra that has quiver with relations depending on the four parameters $ bar{r}=(r_0,r_1,r_2,k)$ with $r_0,r_1,r_2geq 2$ and $kgeq 1$.
Let $mathbf{k}$ be an algebraically closed field of arbitrary characteristic, let $Lambda$ be a finite dimensional $mathbf{k}$-algebra and let $V$ be a $Lambda$-module with stable endomorphism ring isomorphic to $mathbf{k}$. If $Lambda$ is self-injec
Let $mathbf{k}$ be a field of arbitrary characteristic, let $Lambda$ be a finite dimensional $mathbf{k}$-algebra, and let $V$ be a finitely generated $Lambda$-module. F. M. Bleher and the third author previously proved that $V$ has a well-defined ver
Let $mathbf{k}$ be field of arbitrary characteristic and let $Lambda$ be a finite dimensional $mathbf{k}$-algebra. From results previously obtained by F.M Bleher and the author, it follows that if $V^bullet$ is an object of the bounded derived catego
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 appli
Let k be an algebraically closed field of positive characteristic, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG of infinite tame representation type. We find all finitely generated kG-modul