6533b854fe1ef96bd12ae7e5
RESEARCH PRODUCT
Identities of PI-Algebras Graded by a Finite Abelian Group
Irina Sviridovasubject
Discrete mathematicsPure mathematicsAlgebra and Number TheoryMathematics::Commutative AlgebraMathematics::Rings and AlgebrasGraded ringElementary abelian groupGraded Lie algebraFiltered algebraDifferential graded algebraIdeal (ring theory)Abelian groupAlgebraically closed fieldMathematicsdescription
We consider associative PI-algebras over an algebraically closed field of zero characteristic graded by a finite abelian group G. It is proved that in this case the ideal of graded identities of a G-graded finitely generated PI-algebra coincides with the ideal of graded identities of some finite dimensional G-graded algebra. This implies that the ideal of G-graded identities of any (not necessary finitely generated) G-graded PI-algebra coincides with the ideal of G-graded identities of the Grassmann envelope of a finite dimensional (G × ℤ2)-graded algebra, and is finitely generated as GT-ideal. Similar results take place for ideals of identities with automorphisms.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 | Communications in Algebra |