ON WEAKLY 1-ABSORBING PRIMARY IDEALS OF COMMUTATIVE SEMIRINGS

Let R be a commutative semiring with $ 1 \neq0$ . In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal overccommutative semirings . A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc \in I$, then $ab \in I $or $c \in \sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. And we need a special type of ideals called k-ideal or subtractive ideal which is helps to prove results related to weakly 1-absorbing primary ideals. A subtractive ideal I of a semiring R is an ideal such that if $ x,x+y\in I$ ,then $ y\in I$