On Deformations of Gorenstein-Projective Modules over Monomial Algebras with no Overlaps

Let $mathbf{k}$ be a field of arbitrary characteristic, let $Lambda$ be a finite dimensional $mathbf{k}$-algebra, and let $V$ be an indecomposable Gorenstein-projective $Lambda$-module with finite dimension over $mathbf{k}$. It follows that $V$ has a well-defined versal deformation ring $R(Lambda, V)$, which is complete local commutative Noetherian $mathbf{k}$-algebra with residue field $mathbf{k}$, and which is universal provided that the stable endomorphism ring of $V$ is isomorphic to $mathbf{k}$. We prove that if $Lambda$ is a monomial algebra without overlaps, then $R(Lambda,V)$ is universal and isomorphic either to $mathbf{k}$ or to $mathbf{k}[[t]]/(t^2)$