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We continue the study of (Abelian)π-regular rings. Some examples ofπ-regular rings are examined into details in relation to the semiprimeness. Next we study theπ-regularity of commutators, introducing C -π-regular rings as a generalization ofπ-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)M n ( R )is C -π-regular; (ii) R isπ-regular; (iii)M n ( R )is stronglyπ-regular; (iv)M n ( R )isπ-regular, whereM n ( 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.

On π -regularity, strong π -regularity and C - π -regularity