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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 third author that $V$ has a well-defined versal deformation ring $R(Lambda, V)$, which is a complete local commutative Noetherian $mathbf{k}$-algebra with residue field $mathbf{k}$. The third author also proved that if $Lambda$ is a Gorenstein $mathbf{k}$-algebra and $V$ is a Cohen-Macaulay $Lambda$-module whose stable endomorphism ring is isomorphic to $mathbf{k}$, then $R(Lambda, V)$ is universal. In this article we prove that the isomorphism class of a versal deformation ring is preserved under singular equivalence of Morita type between Gorenstein $mathbf{k}$-algebras.
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 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 endomorph
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
The Morita equivalences of classical Brauer algebras and classical Birman-Murakami-Wenzl algebras have been well studied. Here we study the Morita equivalence problems on these two kinds of algebras of simply-laced type, especially for them with the
It is well-known that derived equivalences preserve tensor products and trivial extensions. We disprove both constructions for stable equivalences of Morita type.