Matrices play an important role in both pure and applied mathematics. Matrices with entries
in rings have been intensively studied and used (eg, see [22, 87]); as well as matrices with …

A ring is left Gorenstein regular if the classes of left modules with finite projective dimension
and finite injective dimension coincide and the injective and projective finitistic left …

This work contains some new and known results on modules over formal matrix rings. The
main results are presented with proofs. In ring theory, various matrix rings play an important …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. Let C 1 and C 2 be two classes of left A-modules, D 1 and D 2 be two …

Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. We prove that, if T is a right coherent ring, UB has finite flat dimension, UA …

Большое значение матриц для математики и её приложений общеизвестно. Прежде
всего это относится к числовым матрицам. Активно изучаются и используются также …

Abstract Suppose that T=(A 0 UB) is a formal triangular matrix ring, where A and B are rings
and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using …

Let $ T=\biggl (\begin {matrix} A&0\\U&B\end {matrix}\biggr) $ be a formal triangular matrix
ring, where $ A $ and $ B $ are rings and $ U $ is a $(B, A) $-bimodule. We prove that:(1) If …

We establish connections between (co, weak) silting modules over a ring R and (co, weak)
silting modules over a trivial extension of R. As applications, we describe how to construct …

Abstract Let $ A $ and $ B $ be rings, $ U $ a $(B, A) $-bimodule, and $ T=\left (\begin
{smallmatrix} A & 0\\U & B\\\end {smallmatrix}\right) $ the triangular matrix ring. In this paper …