ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS - (:unkn) unknown (KOREAN MATHEMATICAL SOC, 2014)
Let R be a commutative ring with 1 not equal 0. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever a, b,c is an element of R and abc is an element of I, then ab is an element of I or ac is an element of root I or bc is an element of root I. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.
Keywords: primary ideal; prime ideal; 2-absorbing ideal; n-absorbing ideal