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Eventually semisimple weak F I -extending modules

Figen Takıl Mutlu, Adnan Tercan, Ramazan Yaşar (2023)

Mathematica Bohemica

In this article, we study modules with the weak F I -extending property. We prove that if M satisfies weak F I -extending, pseudo duo, C 3 properties and M / Soc M has finite uniform dimension then M decomposes into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the weak F I -extending, pseudo duo, C 3 properties and ascending (or descending) chain condition on essential submodules then M = M 1 ⊕ M 2 for some semisimple submodule M 1 and Noetherian (or Artinian, respectively)...

FC-modules with an application to cotorsion pairs

Yonghua Guo (2009)

Commentationes Mathematicae Universitatis Carolinae

Let R be a ring. A left R -module M is called an FC-module if M + = Hom ℤ ( M , ℚ / ℤ ) is a flat right R -module. In this paper, some homological properties of FC-modules are given. Let n be a nonnegative integer and ℱ𝒞 n the class of all left R -modules M such that the flat dimension of M + is less than or equal to n . It is shown that ( ⊥ ( ℱ𝒞 n ⊥ ) , ℱ𝒞 n ⊥ ) is a complete cotorsion pair and if R is a ring such that fd ( ( R R ) + ) ≤ n and ℱ𝒞 n is closed under direct sums, then ( ℱ𝒞 n , ℱ𝒞 n ⊥ ) is a perfect cotorsion pair. In particular, some known results are obtained as corollaries....

Honest submodules

Pascual Jara (2007)

Czechoslovak Mathematical Journal

Lattices of submodules of modules and the operators we can define on these lattices are useful tools in the study of rings and modules and their properties. Here we shall consider some submodule operators defined by sets of left ideals. First we focus our attention on the relationship between properties of a set of ideals and properties of a submodule operator it defines. Our second goal will be to apply these results to the study of the structure of certain classes of rings and modules. In particular...

Injective and projective properties of R [ x ] -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

We study whether the projective and injective properties of left R -modules can be implied to the special kind of left R [ x ] -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.

Kappa-Slender Modules

Radoslav Dimitric (2020)

Communications in Mathematics

For an arbitrary infinite cardinal κ , we define classes of κ -cslender and κ -tslender modules as well as related classes of κ -hmodules and initiate a study of these classes.

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