On the Biordered set of Rings

P. G. Romeo a,∗ and R. Akhila b

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.