Group Gradings on Full Matrix Rings

On Projective Geometry over Full Matrix Rings

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...

Differential Polynomial Rings of Triangular Matrix Rings

On gradings of matrix algebras and descent theory

The aim of this paper is to investigate group gradings of matrix algebras. Let k be a field and G be a group. A k-algebra A is called G-graded if A = ⊕g∈GAg, a direct sum of k-subspaces, such that AgAh ⊆ Agh for any g,h ∈ G. Several papers have been devoted to constructing and classifying group gradings on the matrix algebra Mm(k). One can view the algebra Mm(k) as a quotient of the path algebr...

Group Gradings on Simple Lie Algebras in Positive Characteristic

In this paper we describe all gradings by a finite abelian group G on the following Lie algebras over an algebraically closed field F of characteristic p = 2: sln(F ) (n not divisible by p), son(F ) (n ≥ 5, n = 8) and spn(F ) (n ≥ 6, n even).

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.