On closed and absolutely closed varieties of posemigroups

Abstract

In this paper, we first show that the variety [Formula: see text] of posemigroups satisfying an identity [Formula: see text] is closed if it is [Formula: see text]-convex. Next, we show that inverse posemigroups satisfying an identity [Formula: see text] are absolutely closed. We also show that a convex variety of left [right] zero posemigroups is absolutely closed and finally [Formula: see text] is absolutely closed if so is [Formula: see text].