… Let A and B be two rings. For any bimodule AMB, we write T for the upper triangular matrix
ring (AM … Such rings play an important role in the study of the representation theory of artin …

… C is called cotorsion if ExtRF, Cfi º 0 for all flat modules F. We explicitly describe cotorsion
… For example we show that Z, Wfig is cotorsion over T if and only if ZA and WB are cotorsion. …

… For any bimodule AMB, we write T for the upper triangular matrix ring (… pairs over triangular
matrix rings. Mao [22] constructed a complete duality pair DT of T-modules using duality pairs …

… Morita equivalent to an upper triangular matrix ring of degree two over a division ring (see […
Finally, we apply our result to the study of cotorsion theories over von Neumann regular rings. …

… a Noetherian ring of Krull dimension 1. The original motivation for our study of the cotorsion
and contraadjusted modules comes from algebraic geometry. Given a commutative ring R, …

… We denote by T the triangular matrix ring ( A 0 … Enochs and Torrecillas [5] described flat
covers and cotorsion … via the existed construction of upper triangular matrix Artin algebras. Finally…

… Cotilting modules over artinian rings. In this section we characterise cotilting modules over
artinian rings in terms of their indecomposable direct summands. First we recall the definition …

… of Gorenstein-projective modules over triangular matrix rings, Xiong and Zhang developed
a method of constructing semi-Gorenstein-projective modules over triangular matrix rings. …

… pair is precisely bi-complete and AC-Gorenstein rings are determined by such a bi-complete
duality pair (… ⊥ (Am)R, (Am)R) is forms a hereditary cotorsion pair which is cogenerated by …

… cotorsion pair), we are then led to an unexpected class of rings: rings that are orders in perfect
rings (… Accordingly, we are studying rings that are almost perfect in the sense that they are …