Inner homomorphisms and positive-conditional terms (Q2773679)

Criteria are established for two finite or uniformly locally finite algebras of a finite signature to be positive-conditionally rational equivalent (in terms of semigroups of inner homomorphisms of these algebras) and for two finite algebras to be strongly similar (in terms of expanded semigroups of inner homomorphisms of those algebras). The results originate from the author's article [Algebra Logic 37, No. 4, 245-259 (1998; Zbl 0913.08008)], where, for finite algebras, it was proven that the semigroups of inner isomorphisms play the role of invariants for a conditional local equivalence relation on those algebras.