• Title, Summary, Keyword: invertible submodule

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t-Prüfer Modules

  • Kim, Myeong Og;Kim, Hwankoo;Oh, Dong Yeol
    • Kyungpook Mathematical Journal
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    • v.53 no.3
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    • pp.407-417
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    • 2013
  • In this article, we characterize t-Pr$\ddot{u}$fer modules in the class of faithful multiplication modules. As a corollary, we also characterize Krull modules. Several properties of a $t$-invertible submodule of a faithful multiplication module are given.

Multiplication Modules and characteristic submodules

  • Park, Young-Soo;Chol, Chang-Woo
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.321-328
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    • 1995
  • In this note all are commutative rings with identity and all modules are unital. Let R be a ring. An R-module M is called a multiplication module if for every submodule N of M there esists an ideal I of R such that N = IM. Clearly the ring R is a multiplication module as a module over itself. Also, it is well known that invertible and more generally profective ideals of R are multiplication R-modules (see [11, Theorem 1]).

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A HOMOLOGICAL CHARACTERIZATION OF KRULL DOMAINS

  • Wang, Fang Gui;Zhou, De Chuan
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.649-657
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    • 2018
  • Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.