We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
ON WEAKLY RIGHT PRIMARY IDEALS.
- Authors
Groenewald, Nico
- Abstract
Weakly primary ideals in a commutative ring have been introduced and studied by Atani S. Ebrahimi and Farzalipour F. Here we study weakly (principally) right primary ideals in a non-commutative ring. We define a proper ideal P of the ring R to be weakly (principally) right primary if whenever A and B are (principal) ideals of R such that {0} 6= AB ⊆ P, then either A ⊆ P or Bn ⊆ P for some positive integer n depending on A and B. If R is a commutative ring then I is a weakly primary ideal if and only if it is a weakly (principally) right primary ideal. Hence coresponding results about weakly primary ideals will follow as special cases from results proved in this note. We show that if P is an ideal of R such P² = {0} then P is principally right primary if and only if P is weakly principally right primary. If P is a weakly principally right primary ideal which is not a principally right primary ideal of R, then R is 2-primal if and only if P is a 2-primal ideal. We also prove a version of Nakayama's Lemma.
- Subjects
NONCOMMUTATIVE rings; COMMUTATIVE rings
- Publication
Palestine Journal of Mathematics, 2022, Vol 11, Issue 4, p282
- ISSN
2219-5688
- Publication type
Article