Characterizing semigroups $X$ with commutative extensions $\varphi(X)$, $\lambda(X)$, $N_2(X)$, $\upsilon(X)$

Abstract

We characterize semigroups $X$ whose semigroups of filters $\varphi(X)$, maximal linked systems $\lambda(X)$, linked upfamilies $N_2(X)$, and upfamilies $\upsilon(X)$ are commutative.