A non radical based approach to study of associative algebras
arXiv:math/0212369
Abstract
We study pairs of associative algebras and linear functionals. New results together with corrected proofs for previously published material are presented. In particular, we prove the identity ind Mat(n) (#) A=n * ind A$ for finite-dimensional unital associative algebra A with index 1. [ Symbol (#) denotes tensor product ]
40 pages; text has been significantly expanded. Added new sections discussing interaction with radical methods and open problems