Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Group Theory

arXiv:2210.04970 (math)
[Submitted on 10 Oct 2022]

Title:On Hopfian(co-Hopfian) and Fitting S-acts (I)

Authors:Mohammad Roueentan, Roghaieh Khosravi
View PDF
Abstract:The main purpose of the present work is an investigation of the notions Hopfian (co-Hopfian) acts whose their surjective (injective) endomorphisms are isomorphisms. While we investigate conditions that are relevant to these classes of acts, their interrelationship with some other concepts for example quasi-injective and Dedekind-finite acts is studied. Using Hopfian and co-Hopfian concepts, several conditions are given for a quasi-injective act to be Dedekind-finite. Moreover we bring out some properties of strongly Hopfian and strongly co-Hopfian $S$-acts. Ultimately we introduce and study the concept of Fitting acts and over a monoid $S$, some equivalent conditions are found to have all its finitely generated (cyclic) acts Fitting. It is shown that an $S$-act is Fitting if and only if it is both strongly Hopfian and strongly co-Hopfian.
Comments: 13 pages
Subjects: Group Theory (math.GR)
MSC classes: 20M30
Cite as: arXiv:2210.04970 [math.GR]
  (or arXiv:2210.04970v1 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.2210.04970

Submission history

From: Mohammad Roueentan [view email]
[v1] Mon, 10 Oct 2022 19:07:50 UTC (10 KB)
Full-text links:

Access Paper:

license icon view license
Current browse context:
math.GR
< prev   |   next >
new | recent | 2022-10
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)