Recall that monomorphisms in some categories such as the category of posets, and the
category of topological spaces, are not necessarily embeddings. The notion of regular …

Essentiality in the Category of S-acts Page 1 EUROPEAN JOURNAL OF PURE AND APPLIED
MATHEMATICS Vol. 9, No. 1, 2016, 19-26 ISSN 1307-5543 –www.ejpam.com Essentiality in …

Some of the so called smallness conditions in algebra as well as in category theory, are
important and interesting for their own and also tightly related to injectivity, are essential …

Let M be a class of (mono) morphisms in a category A. To study mathematical notions, such
as injectivity, tensor products and flatness, one needs to have some categorical and …

Although the Baer Criterion for injectivity is true for modules over a ring with an identity, it
is an open problem for acts over a semigroup $ S $(with or without identity). In this work …

‌‌The investigation of equational compactness was initiated by‌ ‌Banaschewski and Nelson‌.
‌They proved that pure injectivity is‌ ‌equivalent to equational compactness‌. ‌Here we define …

Injectivity with respect to pure monomorphisms was studied before in categories of modules
and categories of acts. In this paper we study this notion with respect to sequentially pure …

In this paper we take A to be the category Pos-S of S-posets, for a posemigroup S, M< sub>
pd to be the class of partially ordered sequantially-dense monomorphisms and study the …

In this paper, we show that injectivity with respect to the class $\mathcal {D} $ of dense
monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary …

Let M be a class of (mono) morphisms in a category A. To study mathematical notions, such
as injectivity, tensor products and flatness, one needs to have some categorical and …