Jordan isomorphisms of upper triangular matrix rings

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.

Differential Polynomial Rings of Triangular Matrix Rings

Ela 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.

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...

On Jordan Isomorphisms of 2-torsion Free Prime Gamma Rings

This paper defines an isomorphism, an anti-isomorphism and a Jordan isomorphism in a gamma ring and develops some important results relating to these concepts. Using these results we prove Herstein’s theorem of classical rings in case of prime gamma rings by showing that every Jordan isomorphism of a 2-torsion free prime gamma ring is either an isomorphism or an anti-isomorphism. AMS Mathematic...