Abstract
Let K<X> be the free associative algebra freely generated by a countable set of symbols X= {x 1, x 2,…} over a field K of characteristic 0. The element f (x 1,…, x m ) ∈ K<X> is called a polynomial identity for a K-algebra R if f(r 1…r m ) = 0 for all r 1…, r m ∈ R. The set T(R) = {f(x 1,…, x m ) ∈ K<X> | f is a polynomial identity for R} is a two-sided ideal of K<X> which is invariant under all endomorphisms of K<X> and is called a T-ideal. When T(R) ≠ 0, i.e. R satisfies a non-trivial polynomial identity, R is a PI-algebra. The class var R of all algebras satisfying the identities from T(R) is called the variety of algebras generated by R.
One of the talks given by the author at the Seminar on Computational Algebra of the Department of Mathematics of the II University of Rome (Tor Vergata) in April–May 1990.
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Drensky, V. (1990). Polynomial Identities for 2 × 2 Matrices. In: Cattaneo, G.M.P., Strickland, E. (eds) Topics in Computational Algebra. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3424-8_6
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