Volkov, MikhailSilva, PedroSoares, Filipa2018-12-072018-12-072018VOLKOV, Mikhail V.; SILVA, Pedro V.; SOARES, Filipa – Local finiteness for Green's relations in semigroup varieties. Communications in Algebra. ISSN 0092-7872. Vol. 46, N.º 11 (2018), pp. 4625-46530092-78721532-4125http://hdl.handle.net/10400.21/9140A semigroup variety 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 in this variety has only finitely many 𝒦-classes. We characterize locally 𝒦-finite varieties of finite axiomatic rank in the language of “forbidden objects”.engGreen's relationLocal finitenessFinitude localRelações de Greenjournal article10.1080/00927872.2018.1448850