Matrix-rings play a fundamental role in mathematics and its applications. A difficult question is to decide whether a given ring is isomorphic to a matrixring or one of its variants. Several “hidden matrix-rings” have been shown in the literature (see [5]). These rings did not appear as being matrix-rings at the first sight, nevertheless they proved out to be isomorphic to matrix-rings. Another...

Verardi’s construction of special groups of prime exponent is generalized, and put into a context that helps to decide isomorphism problems and to determine the full group of automorphisms (or at least the corresponding orbit decomposition). The groups in question may be interpreted as groups of unitriangular matrices over suitable rings. Finiteness is not assumed.

We describe a new method of describing the pucker of an N-member monocyclic ring using N - 3 parameters. To accomplish this, three ring atoms define a reference plane, and the remainder of the ring is decomposed into triangular flaps. The angle of incidence for each flap upon the reference plane is then measured. The combination of these angles is characteristic of the ring's pucker. This pucke...

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 )

We introduce Backstr\"om pairs and rings, study their derived categories construct for them a sort of categorical resolutions. For the latter we define global dimension, semi-orthogonal decomposition category deduce that dimension ring is at most $2$. Using this decomposition, description module as elements special bimodule. also partial tilting pair to triangular matrices latter.

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...