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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 $M=\oplus_{i\in I}M_i$ such that: (i) all $M_i$ are uniform; (ii) this decomposition of $M$ complements uniform direct summands; (iii) for all $i, j\in I, i\not = j, M_i$ can not be proper embedded in $M_j$; and (iv) $M$ has $1-C_1$. 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 $(1-C_1)$.