Monomial conditions on prime rings

The study of pivotal monomials (and related conditions) is continued and extended, with the aim of studying carefully a situation generalizing Martindale's theory of prime rings with generalized polynomial identity. This is used to describe various classes of rings in terms of simple elementary sentences. The focus is on prime “Johnson” rings, which play a crucial role in our characterizations. It turns out that these rings can be characterized in terms of generalized pivotal monomials, thereby yielding a theory similar to that of [17]. An erratum to this article is available at .