REGULAR SUB-SEQUENTIALLY DENSE INJECTIVE IN THE CATEGORY OF S-POSETS

Abstract

Sequentially dense monomorphisms were first introduced and studied by Giuli for projection algebras and followed by Ebrahimi, Mahmoudi, Moghaddasi and Shahbaz for S-acts.  In this paper we use the notion of sub-Cauchy sequences and introduce the class of regular sub-sequentially dense monomorphisms for S-posets, denoted by \(\mathcal{M}\)_s.  We investigate the properties of the class \(\mathcal{M}\)_s and study \(\mathcal{M}\)_s-injectivity of S-posets.  Further, we find \(\mathcal{M}\)_s-injective hull of S-posets over some kind of semigroups.