A ring R is called right strong stably finite (r.ssf) if for all n ≥ 1, injective endomorphisms of R (n) R are essential. If R is an r.ssf ring and e is an idempotent of R such that eR is a retractable R-module, then eRe is an r.ssf ring. A direct product of rings is an r.ssf ring if and only if each factor is so. The R.ssf condition is investigated for formal triangular matrix rings. In partic...

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring Tn(R,α). By using an ideal theory of a skew triangular matrix ring Tn(R,α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x;α]/〈xn〉, for each positive integer n, where R[x;α] is the skew polynomial ring, and 〈xn〉 is the ideal generated by xn.

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

we introduce the class of “right almost v-rings” which is properly between the classes of right v-rings and right good rings. a ring r is called a right almost v-ring if every simple r-module is almost injective. it is proved that r is a right almost v-ring if and only if for every r-module m, any complement of every simple submodule of m is a direct summand. moreover, r is a right almost v-rin...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )

This paper aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A⋊Γ, and obtain results on block decomposition, complete r...