Ordering Orders and Quotient Rings

Alexander Guterman, László Márki, Pavel Shteyner

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In the present paper, we introduce a general notion of quotient ring which is based on inverses along an element. We show that, on the one hand, this notion encompasses quotient rings constructed using various generalized inverses. On the other hand, such quotient rings can be viewed as Fountain–Gould quotient rings with respect to appropriate subsets. We also investigate the connection between partial order relations on a ring and on its ring of quotients.

Original languageEnglish
Title of host publicationSemigroups, Categories, and Partial Algebras - ICSAA 2019
EditorsP. G. Romeo, Mikhail V. Volkov, A. R. Rajan
Number of pages17
ISBN (Print)9789813348417
StatePublished - 2021
Externally publishedYes
EventInternational Conference on Semigroups and Applications, ICSAA 2019 - Kochi, India
Duration: 9 Dec 201912 Dec 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational Conference on Semigroups and Applications, ICSAA 2019

Bibliographical note

Funding Information:
L. Márki’s research was partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH, grant no. 119934. P. Shteyner is grateful to the BASIS Foundation grant 19-8-2-35-1.

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.


  • Order relations
  • Quotient rings


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