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In the paper, we define(inco) project modules of relatively hereditary torsion theory Υ by intersection complement of module and study their properties; secondly, we define the(inco) Υ-semisimple ring by(inco) Υ-projective module and study their properties. When Υ is a trivial torsion theory on R-rood, we prove that R is a semisimple ring if and only if R is a(inco) semisimple ring and satisfies(inco) condition. 相似文献
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Letτbe a torsion theory on R-mod and M be a left R-mod. In this paper theτ-cotorsionfree radical Cτ(M) of M is studied. When r is stable, the construction and the supplementing radical of Cτ(M) are obtained. 相似文献
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