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On π-regularity, strong π-regularity and C-π-regularity
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AI
DOI：10.1080/00927872.2025.2583321.png)
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Abstract
En 中文
We continue the study of (Abelian) pi-regular rings. Some examples of pi-regular rings are examined into details in relation to the semiprimeness. Next we study the pi-regularity of commutators, introducing C -pi-regular rings as a generalization of pi-regular and C-regular rings. The class of C-pi-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) M-n(R) is C-pi-regular; (ii) R is pi-regular; (iii) M-n(R) is strongly pi-regular; (iv) M-n(R) is pi-regular, where M-n(R) (n >= 2) is the n by n full matrix ring over R. The C-pi-regularity of ordinary ring extensions is also examined through proper examples.
Keywords:
p-regular ring
strongly pi-regular ring
2-primal ring
Abelian ring
C-pi-regular ring
commutator
matrix ring
NI ring
polynomial ring
Journal
C
IF:
0.6
Papers:
271
Citations:
0