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GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC#.
- Source :
- Communications in Algebra; Apr2005, Vol. 33 Issue 4, p1011-1022, 12p
- Publication Year :
- 2005
-
Abstract
- The algebras M a , b ( E ) ? E and M a + b ( E ) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984–1987 (see Kemer 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M 1, 1 ( E ) ? E and M 2 ( E ) when the base field is infinite and of characteristic p > 2. The algebra M a , a ( E ) ? E satisfies certain graded identities that are not satisfied by M 2 a ( E ). In another paper we proved that the algebras M 1, 1 ( E ) and E ? E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 33
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 17000376
- Full Text :
- https://doi.org/10.1081/AGB-200053801