Commutative semigroups with lattice of subsemigroups satisfies a nontrivial identity

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.
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