Search results for "T-IDEALS"

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Varieties of almost polynomial growth: classifying their subvarieties

2007

Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).

Discrete mathematicsPure mathematicsJordan algebraCODIMENSION GROWTHSubvarietyGeneral MathematicsTriangular matrixUniversal enveloping algebraIDENTITIESPI-ALGEBRASAlgebra representationDivision algebraCellular algebraComposition algebraT-IDEALSMathematics
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Varieties of algebras of polynomial growth

2008

Let V be a proper variety of associative algebras over a field F of characteristic zero. It is well-known that V can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of var(G) and var(UT 2), where G is the Grassmann algebra and UT2 is the algebra of 2 x 2 upper triangular matrices.

Settore MAT/02 - Algebrapolynomial identity codimensions.Codimensions T-ideals
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