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Local finiteness for Green's relations in semigroup varieties

Soares, Filipa; Silva, Pedro V.; Volkov, Mikhail V.

Communications in Algebra, 40 (10) (2018), 4625-4653

A semigroup variety V is said to be locally K-finite, where K stands for any of Green's relations H, R, L, D, or J, if every finitely generated semigroup from V has only finitely many K-classes. We characterize locally K-finite varieties of finite axiomatic rank in the language of "forbidden objects".