In the present paper, we study varieties consisting of bands (idempotent semigroups) endowed with an involutorial antiautomorphism * as a fundamental operation. Our principal aim is here to provide an insight to some classes of these varieties from the structural point of view, especially in terms of semilattice decompositions, subdirect products and ideal extensions. In the course of such considerations, we shall extend the result of C. L. Adair [1], who described the lattice of all varieties of bands with a regular involution (i.e. with the identity x = xx* x). We depict a broader lattice of involution band varieties, which incorporates Adair's lattice. [References: 22]
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