On $TL$-bi-ideals of ternary semigroups

G.Mohanraj1* and M.Vela2

doi:10.26637/MJM0602/0024

On $TL$-bi-ideals of ternary semigroups

Authors :

G.Mohanraj^1* and M.Vela²

Author Address :

^1,2Department of Mathematics, Annamalai University, Annamalainagar-608 002, Tamilnadu, India.

*Corresponding author.

Abstract :

We introduce the notions of $TL$-ternary subsemigroup and $TL$-bi-ideals of a ternary semigroup. We redefine $TL$-ternary subsemigroup and $TL$-bi-ideals using $T$-product on $L$-sets .We introduce the notion of $T$-intersection of $L$-sets. We establish that $T$-intersection of two $TL$-bi-ideals is again a $TL$-bi-ideal. We establish necessary and sufficient conditions for a pre-image of $L$-set under homomorphism to be a $TL$-ideal. We introduce the notion of $TL$-level sets. We characterize $TL$-bi-ideal by $TL$-level sets.

Keywords :

$T$-norm, $L$-set, $TL$-subsemigroup, $TL$-bi-ideal, $TL$-level set.

DOI :

10.26637/MJM0602/0024

Article Info :

Received : August 24, 2017; Accepted : February 13, 2018.