On the Biordered set of Rings
Authors :
P. G. Romeo a,∗ and R. Akhila b
Author Address :
a,b Department of Mathematics, Cochin University of Science and Technology, Kochi, Kerala, INDIA.
*Corresponding author.
Abstract :
In [4] K.S.S. Nambooripad introduced biordered sets as a partial algebra $(E, \omega^r, \omega^l)$ 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.
DOI :
Article Info :
Received : November 24, 2015; Accepted : April 15, 2016.