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.
Categories: math.RT