Weak-injectivity and almost perfect domains

Our main purpose is to characterize the class of almost perfect domains (introduced by Bazzoni and Salce [S. Bazzoni, L. Salce, Almost perfect domains, Colloq. Math. 95 (2003) 285–301]) by weak-injectivity. Weak-injective modules have been discussed by Lee [S.B. Lee, Weak-injective modules, Comm. Algebra 34 (2006) 361–370; S.B. Lee, A note on the Matlis category equivalence, J. Algebra 299 (2006) 854–862]. Here we add some more results on weak-injective modules before we give several characterizations of almost perfect domains.