COMMUTATIVE SEMIGROUPS WHOSE LATTICE OF SUBSEMIGROUPS SATISFIES A NONTRIVIAL IDENTITY
Vladimir B. Repnitskiǐ, S. I. Katsman · Mathematics of the USSR-Sbornik · 1990
A description of commutative semigroups whose lattice of subsemigroups satisfies a nontrivial identity is obtained. In particular, an affirmative answer is given to a question of L. N. Shevrin on periodicity of an arbitrary semigroup whose lattice of subsemigroups satisfies a nontrivial identity. As a corollary of the technique developed herein a number of lattice-theoretic facts (known, as well as new) are also obtained. Bibliography: 11 titles.