An R-module M is called an extending module, and also called CS, if it satisfies the following full extending property: For any submodule X of M, there exists a direct summand X \* of M, which is an essential extension of X. The concept of this module is a notable property of injective modules, quas
Some First Order Properties of Direct Sums of Modules
β Scribed by Phillip Olin
- Publisher
- John Wiley and Sons
- Year
- 1970
- Tongue
- English
- Weight
- 787 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let A, B, and C be modules over a unital ring R such that C is Noetherian and Even though A and B need not be isomorphic, we show that they have isomorphic submodule series, and, equivalently, that A and B are indistinguishable by functions on the category of R-modules that respect short exact sequ
Our investigation into the endo-structure of infinite direct sums iβ I M i of indecomposable modules M i -over a ring R with identity-is centered on the following question: If S = End R iβ I M i , how much pressure, in terms of the S-structure of iβ I M i , is required to force the M i into finitely