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Finitely Presented Modules over Right Non-Singular Rings

2008
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Rendiconti del Seminario Matematico della Universita di Padova
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This paper characterizes the right non-singular rings R for which M=Z(M) is projective whenever M is a cyclically (finitely) presented module. Several related results investigate right semi-hereditary rings. b) A a): Let I be the -closure of rR for some r P R. Since R=rR is RDprojective, and R=I (R=rR)=Z(R=rR), we obtain that R=I is projective. Thus, I is generated by an idempotent. By [3, Lemma 3.5], it suffices to show that every -closed right ideal J of R is generated by an idempotent. For

doi:10.4171/rsmup/120-3
fatcat:54mf6eiazbf2fgj6amgn7vspga