Relationships among quasivarieties induced by the min networks on inverse semigroups

Abstract: A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $\rho_k$ and $\rho_t$ the least congruence on $S$ having the same kernel and the same trace as $\rho$, respectively, and denoting by $\omega$ the universal congruence on $S$, we consider the sequence $\omega$, $\omega_k$, $\omega_t$, $(\omega_k)_t$, $(\omega_t)_k$, $((\omega_k)_t)_k$, $((\omega_t)_k)_t$, $\cdots$. The quotients ${S/\omega_k}$, ${S/\omega_t}$, ${S/(\omega_k)_t}$, ${S/(\omega_t)_k}$, ${S/((\omega_k)_t)_k}$, ${S/((\omega_t)_k)_t}$, $\cdots$, as $S$ runs over all inverse semigroups, form quasivarieties. This article explores the relationships among these quasivarieties.