Local finiteness for Green's relations in semigroup varieties

2017/11/21 by Mikhail V. Volkov, Volkov, Mikhail V., Pedro V. Silva +3
Computer Science · #20M07 #Advanced Algebra and Logic #FOS: Mathematics #Group Theory (math.GR) #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1711.07636

openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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".

Related

• Local finiteness for Green relations in (I-)semigroup varieties
• Global local covers
• Local finiteness in varieties of MS4-algebras
• Restrictions on local embeddability into finite semigroups
• Proofs of definability of some varieties and sets of varieties of semigroups