On π -regularity, strong π -regularity and C - π -regularity
Abstract
We continue the study of (Abelian) π-regular rings. Some examples of π-regular rings are examined into details in relation to the semiprimeness. Next we study the π-regularity of commutators, introducing C -π-regular rings as a generalization of π-regular and C-regular rings. The class of C-π-regular rings is shown to be quite large in the procedure. It is proved that for a 2-primal R, the following conditions are equivalent: (i) Mn(R) is C-π-regular; (ii) R is π-regular; (iii) Mn(R) is strongly π-regular; (iv) Mn(R) is π-regular, where Mn(R) (n≥2) is the n by n full matrix ring over R. The C-π-regularity of ordinary ring extensions is also examined through proper examples.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Topics in Algebra
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 6
- Pages
- 2479–2494
- Publication date
- 3 February 2026
- Language
- EN