On phi-projective modules and phi-Prufer rings

摘要

In this article, if S denotes a multiplicatively closed set of a commutative ring R, then S-fractional ideals and S-invertible ideals are introduced. Suppose that the nil radical Nil(R) of R is a divided prime ideal. Then phi-torsion free modules and phi-projective modules are introduced and it is shown that a finitely generated nonnil ideal I is phi-invertible if and only if I is phi-projective as R-module. So R is a phi-Prufer ring if and only if each finitely generated nonnil ideal of R is phi-projective. Communicated by Ellen Kirkman