GENERALIZED CAYLEY GRAPH OF UPPER TRIANGULAR MATRIX RINGS

Differential Polynomial Rings of Triangular Matrix Rings

Zero-Divisor Graph of Triangular Matrix Rings over Commutative Rings

Let R be a noncommutative ring. The zero-divisor graph of R, denoted by Γ(R), is the (directed) graph with vertices Z(R)∗ = Z(R)− {0}, the set of nonzero zero-divisors of R, and for distinct x, y ∈ Z(R)∗, there is an edge x → y if and only if xy = 0. In this paper we investigate the zero-divisor graph of triangular matrix rings over commutative rings. Mathematics Subject Classification: 16S70; ...

Isomorphism of Generalized Triangular Matrix-rings and Recovery of Tiles

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...

Generalized module homomorphisms of triangular matrix rings of order three

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 )

Jordan left derivations in full and upper triangular matrix rings

In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.