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Let $\mathbf{k}$ be a fixed field of arbitrary characteristic, and let$\Lambda$ be a finite dimensional $\mathbf{k}$-algebra. Assume that $V$ is aleft $\Lambda$-module of finite dimension over $\mathbf{k}$. F. M. Bleher andthe author previously proved that $V$ has a well-defined versal deformationring $R(\Lambda,V)$ which is a local complete commutative Noetherian ring withresidue field isomorphic to $\mathbf{k}$. Moreover, $R(\Lambda,V)$ is universalif the endomorphism ring of $V$ is isomorphic to $\mathbf{k}$. In this articlewe prove that if $\Lambda$ is a basic connected cycle Nakayama algebra withoutsimple modules and $V$ is a Gorenstein-projective left $\Lambda$-module, then$R(\Lambda,V)$ is universal. Moreover, we also prove that the universaldeformation rings $R(\Lambda,V)$ and $R(\Lambda, \Omega V)$ are isomorphic,where $\Omega V$ denotes the first syzygy of $V$. This result extends the oneobtained by F. M. Bleher and D. J. Wackwitz concerning universal deformationrings of finitely generated modules over self-injective Nakayama algebras. Inaddition, we also prove the following result concerning versal deformationrings of finitely generated modules over triangular matrix finite dimensionalalgebras. Let $\Sigma=\begin{pmatrix} \Lambda & B\\0& \Gamma\end{pmatrix}$ be atriangular matrix finite dimensional Gorenstein $\mathbf{k}$-algebra with$\Gamma$ of finite global dimension and $B$ projective as a left$\Lambda$-module. If $\begin{pmatrix} V\\W\end{pmatrix}_f$ is a finitelygenerated Gorenstein-projective left $\Sigma$-module, then the versaldeformation rings $R\left(\Sigma,\begin{pmatrix} V\\W\end{pmatrix}_f\right)$and $R(\Lambda,V)$ are isomorphic.

On Deformations of Gorenstein-projective modules over Nakayama and triangular matrix algebras