$n$-cotorsion pairs over formal triangular matrix rings

Abstract

Let $\Lambda=\begin{pmatrix}A & 0 \\U & B \end{pmatrix}$ be a formal triangular matrix ring where $A,B$ are rings and $U$ is a $(B,A)$-bimodule. In this paper, we study some special classes over the formal triangular matrix ring $\Lambda$. Further, using these special classes, we construct a left (resp. right) $n$-cotorsion pair over the formal triangular matrix ring $\Lambda$ from left (resp. right) $n$-cotorsion pairs over $A$ and $B$. Finally, we give an example to illustrate our main result.