A Note On Ideals Of a Three-Dimenensional Associative Algebra

In this paper,we shall apply the theory of nilpotent radical toderive Some results about ideals of a three-dimensional associatvealgebra over a field F and of an associative ring of order P^3 where Pis a prime.These results are useful in studying the structure of thealgebra and the ring. THEOREM 1.Let A be a three-dimensional associative algebraover a field F,N(A)the nilpotent radical of A.If N(A)≠O。

Rota-Baxter Operators of Weight 1 on 2×2-matrix Algebras

In this paper we determine all Rota-Baxter operators of weight 1 on 2 ×2- matrix algebras over an algebraically closed field.

Cohomology of Associative H-Pseudoalgebras

We define the cohomology of associative H-pseudoalgebras,and we show that it describes module extensions,abelian pseudoalgebra extensions,and pseudoalgebra first-order deformations.The same results for the special case of associative conformal algebras are also described in details.

Finite Generation of Lie Derived Powers of Skew Lie Algebras

Let A be a finitely generated associative algebra over a field of characteristic different from 2.Herstein asked when the Lie algebra[A,A]is finitely generated.Recently,it was shown that for a finitely generated nil algebra A all derived powers of A are finitely generated Lie algebras.Let K be the Lie algebra of skew-symmetric elements of an associative algebra with involution.We consider all derived powers of the Lie algebra K and prove that for any finitely generated associative nil algebra with an involution,all derived powers of K are finitely generated Lie algebras.

Embedding Countably Generated Algebras into Simple 2-Generated Algebras

In this paper, by using Gr bner-Shirshov bases theories, we prove that each countably generated associative differential algebra （resp., associative λ-algebra, associa- tive Ω-differential algebra） can be embedded into a simple 2-generated associative differ- ential algebra （resp., associative Ωalgebra, associative λ-differential algebra）.

Majorana Representations of Finite Groups

In this paper we give a brief overview of the theory of Majorana representations of finite groups.

Gelfand–Kirillov Dimensions of the Z^2-graded Oscillator Representations of sl(n)

We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors