• M. Parvathi Banu
• D. Radha

The generalisation of semi group into gamma semigroup was introduced by Sen in 1981 and developed some theory like idempotency, commutativity. Sirojkul, Sripakorn et.al.extended many classical notions of gamma semigroups with respect to one sided idempotent property. In this paper, we define two sided near idempotent gamma semigroup (TSNI gamma semi group) along with the equivalence relation λt and ρt . The rectangular definition is also given for a 2-sided near idempotent gamma semigroup with the TFAE that, it will become a gamma semi group with the following identities xγyγzγy = xγy and xγyγxγz = xγz ; xγyγz = xγz ; xγaγb = xγbγa and aγbγx = bγaγx implies that xγa = xγb and aγx = bγx for all x,y in S and a,b in S and γ in Γ. Also it is proved that near commutativity will imply commutative property in a TSIN gamma semigroup. The definitions of left (right) regular and left (right) normal TSIN gamma semi groups are given with the property that left (right) normality will imply left (right) regularity and hence in turn will give the right (left) near commutative property.

Gamma semi group, rectangular idempotent element, two sided near idempotent, left (right) normal near idempotent, left (right) regular near idempotent, near commutative near idempotent semigroup.

"ON TWO SIDED NEAR IDEMPOTENT GAMMA SEMIGROUP", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.1070-1074, February-2019, Available :http://www.jetir.org/papers/JETIRAB06200.pdf

"ON TWO SIDED NEAR IDEMPOTENT 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. pp1070-1074, February-2019, Available at : http://www.jetir.org/papers/JETIRAB06200.pdf