چكيده لاتين :
No need to say that the study of injectivity with respect to different classes of monomorphisms is crucial in any category. Essentiality is an important notion closely related to injectivity. In fact, injectivity is characterized and injective hulls are defined using essentiality. In this paper, the notion of essentiality with respect to down closed embeddings in the category of S-posets is studied. We study five kinds of essentiality with respect to the class of all down closed regular monomorphisms of S-posets, and investigate their relations to dc-injectivity. More precisely, it is proved that dc-injectivity well behaves regarding these essentialities. Finally, we give an explicit description of the dc-injective hulls of S-posets under some conditions.
