Triangular matrix algebras over Hensel 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; ...

Strongly clean triangular matrix rings with endomorphisms

‎A ring $R$ is strongly clean provided that every element‎ ‎in $R$ is the sum of an idempotent and a unit that commutate‎. ‎Let‎ ‎$T_n(R,sigma)$ be the skew triangular matrix ring over a local‎ ‎ring $R$ where $sigma$ is an endomorphism of $R$‎. ‎We show that‎ ‎$T_2(R,sigma)$ is strongly clean if and only if for any $ain‎ ‎1+J(R)‎, ‎bin J(R)$‎, ‎$l_a-r_{sigma(b)}‎: ‎Rto R$ is surjective‎. ‎Furt...

Triangulaizability of Algebras Over Division Rings

differential polynomial rings of triangular matrix rings