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A note on \(c\)-separative modules. (English) Zbl 1135.19300

Summary: A right \(R\)-module \(P\) is \(c\)-separative provided that \(P\oplus P\overset {c}\cong P\oplus Q\Rightarrow P\cong Q\) for any right \(R\)-module \(Q\). We get two sufficient conditions under which a right module is \(c\)-separative. A ring \(R\) is a hereditary ring provided that every ideal of \(R\) is projective. As an application, we prove that every projective right \(R\)-module over a hereditary ring is \(c\)-separative.

MSC:

19A13 Stability for projective modules
13G05 Integral domains
13C10 Projective and free modules and ideals in commutative rings
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