Idempotent distributive semirings with involution

A semiring with involution is a semiring equipped with an involutorial. antiasutomorphism as a fundamental operation. The aim of the present paper is to determine the lattice of all varieties of idempotent and distributive semirings with involution. We start with the description of their structure, which is followed by a complete list of all subdirectly irreducibles. We make a heavy use of general results obtained recently by Dolinka and Vincic [11] on involutorial Plonka sums. Applying these results and some further structural theorems, we construct the considered lattice. It turns out that it has exactly 64 elements.