• D. Radha
• P. Meenakshi
• B. Utthirach Selvi

The concept of semigroup theory was introduced by A.H. Clifford et. al and extended by many authors like Mchean, David et.al. The algebraic theory of commutative semigroup was studied and extended by M. A. Taiclin, A. P. Biryukov. The concept of idempotent commutative semigroup was studied by D. Radha and P. Meenakshi with some structures like semi-regular, normal, quasi-normal on it. In this paper, we have introduced the notion of Idempotent Commutative Gamma Semigroup and the definition of semi gamma regular, semi gamma normal and gamma quasi-normal semigroups. Also it is proved that, an idempotent commutative gamma semigroup is gamma left(right) normal if and only if it is gamma left(right) quasi normal. Any idempotent commutative gamma semigoup is gamma regular if and only if it is gamma normal and gamma left(right) seminormal if and only if it is gamma left(right) semi regular. And any gamma quasi normal is both gamma semi regular, gamma semi normal and converse is also proved as a characterization theorem.

Idempotent element, commutativity, normal, gamma quasi -normal, gamma semi normal, gamma regular, gamma quasi - regular, gamma semi- regular.

"A Study on Idempotent Commutative Gamma Semigroup", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.1059-1063, February-2019, Available :http://www.jetir.org/papers/JETIRAB06198.pdf

"A Study on Idempotent Commutative Gamma Semigroup", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 2, page no. pp1059-1063, February-2019, Available at : http://www.jetir.org/papers/JETIRAB06198.pdf