Affine representability and decision procedures for commutativity theorems for rings and algebras

DOI10.1007/S11856-022-2309-3arXiv2011.00357WikidataQ113899775 ScholiaQ113899775MaRDI QIDQ6352737

Publication date: 31 October 2020

Abstract: We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial identities, there is an algorithm that terminates after a finite number of steps which decides whether these identities force a ring to be commutative. We then revisit old commutativity theorems of Jacobson and Herstein in light of this algorithm and obtain general results in this vein. In addition, we completely characterize the homogeneous multilinear identities that imply the commutativity of a ring.

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

This page was built for publication: Affine representability and decision procedures for commutativity theorems for rings and algebras

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6352737)