R-projective modules over a semiperfect ring
RD Ketkar, N Vanaja - Canadian Mathematical Bulletin, 1981 - cambridge.org
RD Ketkar, N Vanaja
Canadian Mathematical Bulletin, 1981•cambridge.org… A ring is called left perfect if every left R-module has a projective cover. It is well known
that the radical of every left module over a left perfect ring is small. Hence from Theorem 1
and the Proof of Theorem 2 we get … Let P be a projective left R-module over a left perfect
ring R. Then P is a direct sum of cyclic indecomposable …
that the radical of every left module over a left perfect ring is small. Hence from Theorem 1
and the Proof of Theorem 2 we get … Let P be a projective left R-module over a left perfect
ring R. Then P is a direct sum of cyclic indecomposable …
The aim of this paper is to prove the following theorem:Let R be a semiperfect ring. Let Q be a left R -module satisfying (a) Q is R-projective and (b) J(Q) is small in Q. Then Q is projective.
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