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Some characterizations of π-regular rings with no infinite trivial subring

It is shown that a ring R is a π-regular ring with no infinite trivial subring if and only if R is a subdirect sum of a strongly regular ring and a finite ring. Some other characterizations of such a ring are given. Similar result is proved for a periodic ring. As a corollary, it is shown that every δ-ring is a subdirect sum of a Unite ring and a commutative ring. This was conjectured by Putcha and Yaqub.