On equational theories of varieties of anticommutative rings (Q1966192)

The author constructs a finitely based (noncommutative) subvariety \(\mathbb{X}\) of the variety of all associative rings satisfying the identity \(x^2 = 0\). Given a nonrecursive but recursively enumerable set of positive integers \(P\), the author gives an identity \(t(n)\) for every natural number \(n\) such that \(t(n)\) is an identity in \(\mathbb{X}\) iff \(n\in P\). Thus, the problem of determining which are the identities in the variety \(\mathbb{X}\) is undecidable.