**InternationaleJournals**

**Primary Decomposition in A ****r****-Semigroup
**

**A. Gangadhara Rao ^{1}, A. Anjaneyulu^{2},
D. Madhusudhana Rao^{3}.**

Dept. of Mathematics,V S R & N V R College, Tenali, A.P. India. Email: ^{1}raoag1967@gmail.com, ^{2}anjaneyulu.addala@gmail.com, ^{3}dmrmaths@gmail.com

ABSTRACT

In this paper the terms P-primary, primary decomposition of a r-ideal, reduced primary decomposition of a r-ideal in a r-semigroup S areintroduced. If A_{1}, A_{2},
…A_{n} are P-primary r-ideals in a r-semigroup S, then it is proved that is also a P-primary
r-ideal. If a r-ideal A in a r-semigroup S has a primary decomposition, then it is proved that A has a reduced primary
decomposition. Further it is proved that
every Γ-ideal in a (left, right) duo noetherian

Γ-semigroup S has a reduced (right, left)
primary decomposition. If A and B are two
Γ-ideals in a Γ-semigroup S, then it is proved that A* ^{l} *(B) = {

A

P

**International
eJournal of Mathematical Sciences, Technology and Humanities**

**Volume** **2**,
**Issue** **3**, **Pages**: **466 - 479**