Various kinds of regular injectivity for $S$-posets

Abstract

‎In this paper some properties of weak regular injectivity for $S$-posets‎, <br />‎where $S$ is a pomonoid‎, ‎are studied‎. ‎The behaviour‎ <br />‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎Also‎, ‎some‎ <br />‎characterizations of pomonoids over which all $S$-posets are of‎ <br />‎some kind of weakly regular injective are obtained‎. ‎Further‎, ‎we‎ <br />‎give some Baer conditions which state the relation among some‎ <br />‎kinds of weak regular injectivity‎.