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 r...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。展开更多
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 cas...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.展开更多
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 a...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.展开更多
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...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).展开更多
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 harmoni...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展开更多
文摘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。
基金The author was supported by a grant by Conicet,Consejo Nacional de Investigaciones Cientificas y Técnicas(Argentina).Special thanks to my teacher Victor Kac.
文摘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.
基金funded by King Abdulaziz University,Deanship of Scientific Research(grant number RG-50-130-39).
文摘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.
文摘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).
基金Supported by National Natural Science Foundation of China(Grant No.11171324)
文摘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