Sequentially dense monomorphisms and injectivity with respect to these monomorphisms
were first introduced and studied by Giuli for acts over the monoid (N∞, min). In this paper …

Essentiality is an important notion closely related to injectivity. Depending on a class
\mathcalM of morphisms of a category \mathcalA, three different types of essentiality are …

The object of this paper is to generalize the notion of supplement in modules to monoid acts.
In contrast to the case of modules that supplements of submodules do not generally exist …

Projection algebras are M-sets for the monoid M=(ℕ∞, min) which are used by computer
scientists for algebraic specification of process algebras. In contrast to the case of modules it …

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 …

Any notion of purity is normally defined in terms ofsolvability of some set of equations. In this
paper we first take this point of view to introduce a kind of purity, called $ s $-purity, for acts …

The class \mathcalM_d of sequentially dense monomorphisms were first defined and
studied by Giuli, Ebrahimi, and Mahmoudi for projection algebras (acts over the monoid …

This thesis consists of three parts: First, the notion of a weak (Lawvere-Tierney) topology on
an (elementary) topos E is deeply analyzed. We present some essential differeneces …

Banaschewski defines and gives sufficient conditions on a category 𝒜 and a subclass ℳ of
its monomorphisms under which ℳ-injectivity properly behaves with respect to the notions …