2011/08/17 by Yongduo Wang, Wang, Yongduo
Mathematics · #16D10 #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16D10
paper · pdf · doi:10.48550/arxiv.1108.3381
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arxiv created 2011/08/17 · openalex publication_date 2011/08/17 · arxiv updated 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a left module over a ring R and I an ideal of R. M is called an I-supplemented module (finitely I-supplemented module) if for every submodule (finitely generated submodule) X of M, there is a submodule Y of M such that X+Y=M, X∩ Y⊆ IY and X∩ Y is PSD in Y. This definition generalizes supplemented modules and δ-supplemented modules. We characterize I-semiregular, I-semiperfect and I-perfect rings which are defined by Yousif and Zhou [15] using I-supplemented modules. Some well known results are obtained as corollaries.