Abstract
Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.
Original language | English |
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Pages (from-to) | 1843-1857 |
Number of pages | 15 |
Journal | Proceedings of the American Mathematical Society |
Volume | 145 |
Issue number | 5 |
DOIs | |
State | Published - 2017 |
Keywords
- Grassmann algebra
- Involution
- Polynomial identity
- Superinvolution
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- General Mathematics