Quasi-identities of finite semigroups and symbolic dynamics (original) (raw)

This paper explores the quasi-identities of finite semigroups in connection with symbolic dynamics. It provides definitions and foundational concepts in universal algebra, particularly focusing on varieties and quasi-varieties defined by identities and quasi-identities, respectively. The main result demonstrates that for any finite semigroup of height h, its corresponding quasi-variety belongs to a particular class of quasi-varieties, Q_n, when n exceeds h, with implications concerning the structure and behavior of these semigroups and their generated identities.