On the 2-absorbing ideals in commutative rings

Let R be a commutative ring with identity. In this article, we study a generalization of prime ideal. A proper ideal I of R is called a 2-absorbing ideal if whenever abc ? I for a,b,c ? R, then ab ? I or bc ? I or ac ? I. It is shown that if I is a 2-absorbing ideal of a Noetherian ring R, then R=I has some ideals Jn, where 1 ? n ? t and t is a positive integer, such that Jn possesses a prime filtration FJn : 0 ? R(x1+I) ? R(x1+I) ? R(x2+I) ?...? R(x1+I) ?...?

R(xn+I) = Jn with AssR(Jn) = { I :R xi | i = 1; . . . . n} and | AssR(Jn) | = n. Also, a 2-Absorbing Avoidance Theorem is proved.