Page 1

Displaying 1 – 13 of 13

Showing per page

Abelian differential modes are quasi-affine

David Stanovský (2012)

Commentationes Mathematicae Universitatis Carolinae

We study a class of strongly solvable modes, called differential modes. We characterize abelian algebras in this class and prove that all of them are quasi-affine, i.e., they are subreducts of modules over commutative rings.

Centralizing traces and Lie-type isomorphisms on generalized matrix algebras: a new perspective

Xinfeng Liang, Feng Wei, Ajda Fošner (2019)

Czechoslovak Mathematical Journal

Let be a commutative ring, 𝒢 be a generalized matrix algebra over with weakly loyal bimodule and 𝒵 ( 𝒢 ) be the center of 𝒢 . Suppose that 𝔮 : 𝒢 × 𝒢 𝒢 is an -bilinear mapping and that 𝔗 𝔮 : 𝒢 𝒢 is a trace of 𝔮 . The aim of this article is to describe the form of 𝔗 𝔮 satisfying the centralizing condition [ 𝔗 𝔮 ( x ) , x ] 𝒵 ( 𝒢 ) (and commuting condition [ 𝔗 𝔮 ( x ) , x ] = 0 ) for all x 𝒢 . More precisely, we will revisit the question of when the centralizing trace (and commuting trace) 𝔗 𝔮 has the so-called proper form from a new perspective. Using the aforementioned...

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf, Nazia Parveen, Bilal Ahmad Wani (2017)

Communications in Mathematics

Let 𝔄 = 𝒜 be the triangular algebra consisting of unital algebras 𝒜 and over a commutative ring R with identity 1 and be a unital ( 𝒜 , ) -bimodule. An additive subgroup 𝔏 of 𝔄 is said to be a Lie ideal of 𝔄 if [ 𝔏 , 𝔄 ] 𝔏 . A non-central square closed Lie ideal 𝔏 of 𝔄 is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on 𝔄 , every generalized Jordan triple higher derivation of 𝔏 into 𝔄 is a generalized higher derivation of 𝔏 into 𝔄 .

Jordan automorphisms of triangular algebras. II

Driss Aiat Hadj Ahmed, Rachid Tribak (2015)

Commentationes Mathematicae Universitatis Carolinae

We give a sufficient condition under which any Jordan automorphism of a triangular algebra is either an automorphism or an anti-automorphism.

Nonlinear maps preserving Lie products on triangular algebras

Weiyan Yu (2016)

Special Matrices

In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.

Semi-Symmetric Algebras: General Constructions. Part II

Iliev, Valentin Vankov (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 15A69, 15A78.In [3] we present the construction of the semi-symmetric algebra [χ](E) of a module E over a commutative ring K with unit, which generalizes the tensor algebra T(E), the symmetric algebra S(E), and the exterior algebra ∧(E), deduce some of its functorial properties, and prove a classification theorem. In the present paper we continue the study of the semi-symmetric algebra and discuss its graded dual, the corresponding canonical bilinear form,...

Currently displaying 1 – 13 of 13

Page 1