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Abstract
Let R be a ring. A left R-module M (resp. right R-module N) is called singly injective (resp. singly flat) if Ext1(F / C, M) = 0 (resp. Tor1(N, F / C) = 0) for any cyclic submodule C of any finitely generated free left R-module F. It is shown that R is a left pseudo-coherentring if and only if any direct product of singly flat right R-modules is singly flat if and only if any direct limit of singly injective left R-modules is singly injective if and only if every right R-module has a singly flat preenvelope; and every left R-module over a left pseudo-coherent ring R has a singly injective cover. Some applications are also given.
Received: 2008-02-16
Published Online: 2010-02-12
Published in Print: 2010-September
© de Gruyter 2010
