On the biordered set of rings

P. G. Romeo; R. Akhila

doi:10.26637/mjm403/016

Abstract

In [4] K.S.S. Nambooripad introduced biordered sets as a partial algebra \(\left(E, \omega^r, \omega^l\right)\) where \(\omega^r\) and \(\omega^l\) are two quasiorders on the set \(E\) satisfying biorder axioms; to study the structure of a regular semigroup. Later in [2] David Esdown showed that the set of idempotents of a regular semigroup forms a regular biordered set. Here we extend the idea of biordered sets into rings and discussed some of its properties.

Keywords:

Biordered set, Sandwitch set

Mathematics Subject Classification:

20M10

Authors Imprint References Funding Related Articles Downloads

P. G. Romeo Department of Mathematics, Cochin University of Science and Technology, Kochi, Kerala, INDIA. https://orcid.org/0000-0001-9539-7810
R. Akhila Department of Mathematics, Cochin University of Science and Technology, Kochi, Kerala, INDIA.

Pages: 463-467
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

A. H. Clifford and G. B. Preston (1964): The Algebraic Theory of Semigroups, Volume 1 Math. Surveys of the American. Math. Soc.7, Providence, R. I.

David Easdown (1985): Biordered sets comes from Semigroups : Journal of Algebra, 96, 581-591, 87d:06020. DOI: https://doi.org/10.1016/0021-8693(85)90028-6

J. M. Howie (1976): An Introduction To Semigroup Theory, Academic Press Inc. (London). ISBN: 75-46333

K.S.S. Nambooripad (1979): Structure of Regular Semigroups (MEMOIRS, No.224), American Mathematical Society, ISBN-13: 978-0821 82224 DOI: https://doi.org/10.1090/memo/0224