Ordering Orders and Quotient Rings

Alexander Guterman; László Márki; Pavel Shteyner

doi:10.1007/978-981-33-4842-4_1

Ordering Orders and Quotient Rings

Alexander Guterman, László Márki, Pavel Shteyner

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	Semigroups, Categories, and Partial Algebras - ICSAA 2019
Editors	P. G. Romeo, Mikhail V. Volkov, A. R. Rajan
Publisher	Springer
Pages	1-17
Number of pages	17
ISBN (Print)	9789813348417
DOIs	https://doi.org/10.1007/978-981-33-4842-4_1
State	Published - 2021
Externally published	Yes
Event	International Conference on Semigroups and Applications, ICSAA 2019 - Kochi, India Duration: 9 Dec 2019 → 12 Dec 2019

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	345
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Semigroups and Applications, ICSAA 2019
Country/Territory	India
City	Kochi
Period	9/12/19 → 12/12/19

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.

Keywords

Order relations
Quotient rings

Access to Document

10.1007/978-981-33-4842-4_1

Cite this

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Guterman, A, Márki, L & Shteyner, P 2021, Ordering Orders and Quotient Rings. in PG Romeo, MV Volkov & AR Rajan (eds), Semigroups, Categories, and Partial Algebras - ICSAA 2019. Springer Proceedings in Mathematics and Statistics, vol. 345, Springer, pp. 1-17, International Conference on Semigroups and Applications, ICSAA 2019, Kochi, India, 9/12/19. https://doi.org/10.1007/978-981-33-4842-4_1

Ordering Orders and Quotient Rings. / Guterman, Alexander; Márki, László; Shteyner, Pavel.
Semigroups, Categories, and Partial Algebras - ICSAA 2019. ed. / P. G. Romeo; Mikhail V. Volkov; A. R. Rajan. Springer, 2021. p. 1-17 (Springer Proceedings in Mathematics and Statistics; Vol. 345).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ordering Orders and Quotient Rings

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