Weakly distributive modules. Applications to supplement submodules

作者：Buyukasik Engin^*; Demirci Yilmaz M

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2010, 120(5): 525-534.

• Distributive module
• supplement submodule

In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of Ganesan and Vanaja. We prove that pi-projective duo modules, in particular commutative rings, are weakly distributive. Using this result we obtain that in a commutative ring supplements are unique. This generalizes a result of Camillo and Lima. We also prove that any weakly distributive circle plus-supplemented module is quasi-discrete.

• 出版日期2010-11