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.
|Title of host publication||Semigroups, Categories, and Partial Algebras - ICSAA 2019|
|Editors||P. G. Romeo, Mikhail V. Volkov, A. R. Rajan|
|Number of pages||17|
|State||Published - 2021|
|Event||International Conference on Semigroups and Applications, ICSAA 2019 - Kochi, India|
Duration: 9 Dec 2019 → 12 Dec 2019
|Name||Springer Proceedings in Mathematics and Statistics|
|Conference||International Conference on Semigroups and Applications, ICSAA 2019|
|Period||9/12/19 → 12/12/19|
Bibliographical noteFunding 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.
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
- Order relations
- Quotient rings