On ۲-absorbing and weakly ۲-absorbing principally right primary ideals

Let R be a noncommutative ring. The purpose of this note is to investigate the concept of ۲-absorbing (resp., weakly ۲-absorbing) p right primary ideals generalizing ۲-absorbing (resp., weakly ۲-absorbing) ideals of noncommutative rings. From Birkenmeier we have that for commutative rings the notions of primary rings (ideals) coincide with p right primary rings (ideals). Hence all results about ۲-absorbing and weakly ۲-absorbing primary ideals for commutative rings will follow as special cases from results proved in this note. A number of results concerning ۲-absorbing (resp., weakly ۲-absorbing) p right primary ideals are given, generalizing the corresponding results from commutative rings to noncommutative rings.

Keywords:

right primary , weakly right primary , strongly p-nilary , prime ideal