Definable principal congruences and ๐ -stable identities
G. E. Simons ยท Proceedings of the American Mathematical Society ยท 1986
We show that an algebra over an infinite field generates a variety with definable principal congruences if and only if it is commutative. A similar result is proved for polynomial rings. The main tool used is the notion from the theory of PI-rings of an R R -stable identity.