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Let $A=KQ_A/I_A$ and $B=KQ_B/I_B$ be two finite-dimensional bound quiveralgebras, fix two vertices $a\in Q_A$ and $b\in Q_B$. We define an algebra$\Lambda=KQ_\Lambda/I_\Lambda$, which is called a simple gluing algebra of $A$and $B$, where $Q_\Lambda$ is from $Q_A$ and $Q_B$ by identifying $a$ and $b$,$I_\Lambda=\langle I_A,I_B\rangle$. We prove that $\Lambda$ is Gorenstein ifand only if $A$ and $B$ are Gorenstein, and describe the Gorenstein projectivemodules, singularity category, Gorenstein defect category and alsoCohen-Macaulay Auslander algebra of $\Lambda$ from the corresponding ones of$A$ and $B$.

Gorenstein properties of simple gluing algebras