SEQUENTIALLY COMPACT S-ACTS

author

  • H. Barzegar Department of Mathematics, University of Tafresh , 3951879611, Tafresh, Iran.
Abstract:

‎‎The investigation of equational compactness was initiated by‎ ‎Banaschewski and Nelson‎. ‎They proved that pure injectivity is‎ ‎equivalent to equational compactness‎. ‎Here we define the so‎ ‎called sequentially compact acts over semigroups and study‎ ‎some of their categorical and homological properties‎. ‎Some‎ ‎Baer conditions for injectivity of S-acts are also presented‎.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Maximal (sequentially) compact topologies

We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in which convergent sequences have unique limits. We also answer a question of D.E. Cameron by showing that each sequentially compact topology is contained in a ...

full text

Sequentially Compact, Franklin-Rajagopalan Spaces

A locally compact T2-space is called a Franklin-Rajagopalan space (or FR-space) provided it has a countable discrete dense subset whose complement is homeomorphic to an ordinal with the order topology. We show that (1) every sequentially compact FR-space X can be identified with a space constructed from a tower T on w (X = X(T)), and (2) for an ultrafilter u on w, a sequentially compact FR-spac...

full text

Quasi-projective covers of right $S$-acts

In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

full text

Sequentially Dense Essential Monomorphisms of Acts Over Semigroups

The class Md of sequentially dense monomorphisms were first defined and studied by Giuli, Ebrahimi, and Mahmoudi for projection algebras (acts over the monoid (N∞, min), of interest to computer scientists, as studied by Herrlich, Ehrig, and some others) and generalized to acts over arbitrary semigroups. Mdinjectivity has been shown by some of the above authors to be also useful in the study of ...

full text

Intersection Graphs of S-acts

Let S be a semigroup. The intersection graph of an S-act A, denoted by G(A), is the undirected simple graph obtained by setting all non-trivial subacts of A to be the vertices and defining two distinct vertices to be adjacent if and only if their intersection is non-empty. It is investigated the interplay between the algebraic properties of A and the graph-theoretic properties of G(A). Also som...

full text

PFA(S)[S] and countably compact spaces

We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact.

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 5  issue 2

pages  111- 125

publication date 2018-01-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023