On various quasi ideals in $b$-semirings

G. Mohanraj 1 * and M. Palanikumar 2

doi:10.26637/MJM0801/0004

On various quasi ideals in $b$-semirings

Authors :

G. Mohanraj ^{1 *} and M. Palanikumar ²

Author Address :

^1,2 Department of Mathematics, Annamalai University, Annamalai Nagar-608002, Tamil Nadu, India.

*Corresponding author.

Abstract :

We introduce six types of quasi ideals in $b$-semirings. Each quasi ideals generated by single element(set) is established. We characterize various 1-regular(2-regular, regular) by using generalized 1-quasi (generalized 2-quasi, generalized quasi) ideal, 1-quasi (2-quasi, quasi) ideal, weak1(2)-right(left) ideal and weak1(2)-ideal. Examples are provided to strengthen our results.

Keywords :

1-quasi ideal, 2-quasi ideal, generalized 1-quasi ideal, generalized 2-quasi ideal.

DOI :

10.26637/MJM0801/0004

Article Info :

Received : October 14, 2019; Accepted : December 26, 2019.