Generalizations Of 2-Absorbing Principally Right Primary Ideals In Non-Commutative Rings

Let R be a non-commutative ring with 1 not equal 0 and S(R) be the set of all ideals of R. In this paper, we extend the concept of 2-absorbing principally right primary ideals to the context of phi-2-absorbing principally right primary ideals. Let phi : S(R)-* S(R) U {O} be a function. A proper ideal I of R is said to be a phi- 2-absorbing principally right primary ideal of R if whenever a, b, c E R with aRbRc C_ I and aRbRc not subset of phi(I) implies ab E I or ac E I or bc E I. A number of results and characterizations concerning phi-2-absorbing principally right primary ideals are given.