Almost Lie nilpotent non-prime varieties of associative algebras

A variety of associative algebras is called Lie nilpotent if it satisfies the identity [...[[x(1), x(2)], ..., x(n)] = 0 for some positive integer n, where [x, y] = xy - yx. We study almost Lie nilpotent varieties, i.e., minimal elements in the set of all varieties that are not Lie nilpotent. We describe all almost Lie nilpotent varieties of algebras over a field of positive characteristic, both finite and infinite, in the cases when the ideals of identities of these varieties are nonprime in the class of all T-ideals.