A classification of indecomposable Quasi-Frobenius rings I. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Birkenmeier, Gary F.; Almallah, Omar
• Is Part Of: Communications in algebra. Volume 47:Issue 12(2019)
• Page Start: 5121
• Page End: 5132
• Publication Date: 2019-12-02
• Subjects: Quasi-Frobenius ring -- indecomposable ring -- nilary ring -- idempotent; Primary: 16L60 -- 16D50 -- Secondary:16D70; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1612418
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: This is the first in a series of papers on the classification of indecomposable QF-rings. Our classification is based on the concepts of a nilary ring and the essentiality of the traces of idempotent generated right ideals. Recall that a ring R is called nilary if AB = 0 then A is nilpotent or B is nilpotent for all ideals A and B of R . In this paper, we classify the nilary QF-rings.