In the paper,we study algebras having n bilinearmultiplication operations [InlineMediaObject not available: see fulltext.]: A×A → A, s = 1, ..., n, such that (a[InlineMediaObject not available: see fulltext.]b) [InlineMediaObject ...

We prove that every finite-dimensional homogeneously simple associative algebra over an algebraically closed field is representable as the product of a full matrix algebra and a graded field. © Allerton Press, Inc., 2011.

In the paper, some properties of algebras of associative type are studied, and these properties are then used to describe the structure of finite-dimensional semisimple modular Lie algebras. It is proved that the homogeneous ...

We obtain a classification of 2- and 3-dimensional Lie sheaves. © 2013 Allerton Press, Inc.

In the paper, an analog of the Engel theorem for graded algebras admitting a Lie-type module is proved. Moreover, it is shown that every semisimple algebra of associative type with ordered grading and one-dimensional grading ...

We classify simple Lie sheaves of dimension at most 4. © 2014 Pleiades Publishing, Ltd.

© 2016, Pleiades Publishing, Ltd.In terms of sandwich algebras, we obtain a classification of symmetrical simple Lie sheaves over an algebraically closed field of zero characteristic.

We prove an analog of the Lie theorem for finite-dimensional n-tuple solvable Lie algebras over an algebraically closed field of characteristic 0. © 2012 Allerton Press, Inc.