Almost cross varieties of aperiodic monoids with central idempotents. (Q1943346)

A variety of algebras is a `Cross' variety if it is finitely generated, finitely based, and has finitely many subvarieties. A variety is `almost Cross' if it is minimal among non-Cross varieties. Within the class \(\mathcal A\) of aperiodic monoids with central idempotents, two finitely generated almost Cross varieties \(\mathbf{J_1,J_2}\) were found by \textit{M. Jackson} [Semigroup Forum 70, No. 2, 159-187 (2005; Zbl 1073.20052)] and shown by the author [Port. Math. (N.S.) 68, No. 4, 425-429 (2011; Zbl 1241.20068)] to be the only such. (Each has finitely many subvarieties but is not finitely based.) Here the author completes the characterization by introducing an infinitely generated, finitely based variety \(\mathbf L\) with countably infinitely many subvarieties, and showing that is the only additional almost Cross variety within \(\mathcal A\).