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Acta Mathematica Vietnamica

SOME RESULTS ON QUASI-CONTINUOUS MODULES

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Abstract

In [5] Mohamed and Müller introduced and gave some characterizations of quasi-continuous modules. Here we characterize these modules by extending property of uniform submodules. The following theorem is proven: Let M=iIMi such that: (i) all Mi are uniform; (ii) this decomposition of M complements uniform direct summands; (iii) for all i,jI,ij,Mi can not be proper embedded in Mj; and (iv) M has 1C1. Then M is a quasi-continuous module. As an application we show that, a ring R is QF iff R is semiperfect right continuous and every projective right R-module has (1C1).