A Nonhomological Proof of SemiPerfectness in Matrix Rings

Differential Polynomial Rings of Triangular Matrix Rings

A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS

In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...

differential polynomial rings of triangular matrix rings

Presentations of matrix rings

Recently, there has been a significant interest in the combinatorial properties the ring of n×n matrices. The aim of this note is to describe a short (may be the shortest possible) presentation of the matrix ring Matn(Z). This presentation is significantly shorter than the previously known ones, see [7]. Surprisingly, the number of relations in the presentation does not depend on the size of th...

Diagonal Matrix Reduction over Refinement Rings

  Abstract: A ring R is called a refinement ring if the monoid of finitely generated projective R- modules is refinement.  Let R be a commutative refinement ring and M, N, be two finitely generated projective R-nodules, then M~N  if and only if Mm ~Nm for all maximal ideal m of  R. A rectangular matrix A over R admits diagonal reduction if there exit invertible matrices p and Q such that PAQ is...