ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS - (:unkn) unknown (KOREAN MATHEMATICAL SOC, 2015)
Let R be a commutative ring with 1 not equal 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b,c is an element of R and 0 not equal 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 weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.
Keywords: primary ideal; weakly primary ideal; prime ideal; weakly prime ideal; 2-absorbing ideal; n-absorbing ideal; weakly 2-absorbing ideal; 2-absorbing primary ideal; weakly 2-absorbing primary ideal