Generalization of primary ideal associated with a special radical class

Let ρ be a special radical class. In this paper, we introduce the concept of (almost) right primary ideals related to the ρ radical of a ring R , which will be denoted by ρ ( R ) . We discuss certain special properties related to the prime radical P ( R ) and to the Jacobson radical J ( R ) . In cas...

Full description

Saved in:
Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences 2024, Vol.18 (1), p.159-178
Main Authors: Abouhalaka, Alaa, Fındık, Şehmus
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Article
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let ρ be a special radical class. In this paper, we introduce the concept of (almost) right primary ideals related to the ρ radical of a ring R , which will be denoted by ρ ( R ) . We discuss certain special properties related to the prime radical P ( R ) and to the Jacobson radical J ( R ) . In case that ρ ( R ) is the Jacobson radical J ( R ) , we provide a characterization of rings in which every ideal is a right primary J ideal.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-023-00392-6