COMPLETE PURE INJECTIVITY AND ENDOMORPHISM-RINGS

Authors
PARDO JLG DUNG NV WISBAUER R
Citation
Jlg. Pardo et al., COMPLETE PURE INJECTIVITY AND ENDOMORPHISM-RINGS, Proceedings of the American Mathematical Society, 118(4), 1993, pp. 1029-1034
Citations number
20
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
118
Issue
4
Year of publication
1993
Pages
1029 - 1034
Database
ISI
SICI code
0002-9939(1993)118:4<1029:CPIAE>2.0.ZU;2-1
Abstract
It is shown that if M is a finitely presented completely pure injectiv e object in a locally finitely generated Grothendieck category C such that S = End(C) M is von Neumann regular, then S is semisimple. This i s a generalized version of a well-known theorem of Osofsky, which incl udes also a result of Damiano on PCI-rings. As an application, we obta in a characterization of right hereditary rings with finitely presente d injective hull.