ON STRONGLY S-PROJECTIVE MODULES
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Let R be a commutative ring with identity and S a multiplicative subset of R. In this work, we define and study new versions of the u-S-projective module and the u-S-hereditary ring called strongly S-projective module and strongly S-hereditary ring respectively. In this work, a module M is called strongly S-projective if there exists a projective submodule P of M such that sM ⊆ P. Several properties concerning those notions are shown in this study. The exploration of the relationship between the introduced notions and the u-S-projectivity, projectivity, and other classical ones led to important results. For instance, we showed that any strongly S-projective module is u-S-projective.
Abstract
Let R be a commutative ring with identity and S a multiplicative subset of R. In this work, we define and study new versions of the u-S-projective module and the u-S-hereditary ring called strongly S-projective module and strongly S-hereditary ring respectively. In this work, a module M is called strongly S-projective if there exists a projective submodule P of M such that sM ⊆ P. Several properties concerning those notions are shown in this study. The exploration of the relationship between the introduced notions and the u-S-projectivity, projectivity, and other classical ones led to important results. For instance, we showed that any strongly S-projective module is u-S-projective.
참고문헌 (17)
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