Vladikavkazskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vladikavkaz. Mat. Zh., 2021, Volume 23, Number 1, Pages 20–31 (Mi vmj752)  

Topological lattice rings with the $AM$-property

O. Zabeti

University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

Abstract: Motivated by the recent definition of the $AM$-property in locally solid vector lattices [O. Zabeti, doi: 10.1007/s41980-020-00458-7], in this note, we try to investigate some counterparts of those results in the category of all locally solid lattice rings. In fact, we characterize locally solid lattice rings in which order bounded sets and bounded sets agree. Furthermore, with the aid of the $AM$-property, we find conditions under which order bounded group homomorphisms and different types of bounded group homomorphisms coincide. Moreover, we show that each class of bounded order bounded group homomorphisms on a locally solid lattice ring $X$ has the Lebesgue or the Levi property if and only if so is $X$.

Key words: locally solid lattice ring, bounded group homomorphism, $AM$-property, Levi property, Lebesgue property.

DOI: https://doi.org/10.46698/a8913-4331-4311-d

Full text: PDF file (236 kB)
References: PDF file   HTML file

UDC: 517.98
MSC: 13J25, 06F25
Received: 17.05.2019
Language:

Citation: O. Zabeti, “Topological lattice rings with the $AM$-property”, Vladikavkaz. Mat. Zh., 23:1 (2021), 20–31

Citation in format AMSBIB
\Bibitem{Zab21}
\by O.~Zabeti
\paper Topological lattice rings with the $AM$-property
\jour Vladikavkaz. Mat. Zh.
\yr 2021
\vol 23
\issue 1
\pages 20--31
\mathnet{http://mi.mathnet.ru/vmj752}
\crossref{https://doi.org/10.46698/a8913-4331-4311-d}


Linking options:
  • http://mi.mathnet.ru/eng/vmj752
  • http://mi.mathnet.ru/eng/vmj/v23/i1/p20

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Владикавказский математический журнал
    Number of views:
    This page:29
    Full text:7
    References:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021