paper

Relationships among quasivarieties induced by the min networks on inverse semigroups

arXiv:2008.10539 · doi:10.1007/s00233-020-10126-1

Abstract

A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $I ¨ _{k}$ and $I ¨ _{t}$ the least congruence on $S$ having the same kernel and the same trace as $I ¨ $ , respectively, and denoting by $I ¨ $ the universal congruence on $S$ , we consider the sequence $I ¨ $ , $I ¨ _{k}$ , $I ¨ _{t}$ , $(I ¨ _{k})_{t}$ , $(I ¨ _{t})_{k}$ , $((I ¨ _{k})_{t})_{k}$ , $((I ¨ _{t})_{k})_{t}$ , $\dots$ . The quotients ${S / I ¨ _{k}}$ , ${S / I ¨ _{t}}$ , ${S / (I ¨ _{k})_{t}}$ , ${S / (I ¨ _{t})_{k}}$ , ${S / ((I ¨ _{k})_{t})_{k}}$ , ${S / ((I ¨ _{t})_{k})_{t}}$ , $\dots$ , as $S$ runs over all inverse semigroups, form quasivarieties. This article explores the relationships among these quasivarieties.