ﻻ يوجد ملخص باللغة العربية
Let $mathbf{k}$ be an algebraically closed field, and let $Lambda$ be a finite dimensional $mathbf{k}$-algebra. We prove that if $Lambda$ is a Gorenstein algebra, then every finitely generated Cohen-Macaulay $Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $mathbf{k}$ has a universal deformation ring $R(Lambda,V)$, which is a complete local commutative Noetherian $mathbf{k}$-algebra with residue field $mathbf{k}$, and which is also stable under taking syzygies. We investigate a particular non-self-injective Gorenstein algebra $Lambda_0$, which is of infinite global dimension and which has exactly three isomorphism classes of finitely generated indecomposable Cohen-Macaulay $Lambda_0$-modules $V$ whose stable endomorphism ring is isomorphic to $mathbf{k}$. We prove that in this situation, $R(Lambda_0,V)$ is isomorphic either to $mathbf{k}$ or to $mathbf{k}[[t]]/(t^2)$.
Let $Lambda$ be a finite-dimensional algebra over a fixed algebraically closed field $mathbf{k}$ of arbitrary characteristic, and let $V$ be a finitely generated $Lambda$-module. It follows from results previously obtained by F.M. Bleher and the thir
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 a field of arbitrary characteristic, let $Lambda$ be a Gorenstein $mathbf{k}$-algebra, and let $V$ be an indecomposable finitely generated non-projective Gorenstein-projective left $Lambda$-module whose stable endomorphism ring is
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
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