The sum-product splitting property and injective direct sums of modules over von Neumann regular rings
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- by Birge Zimmermann-Huisgen PDF
- Proc. Amer. Math. Soc. 83 (1981), 251-254 Request permission
Abstract:
Let ${({M_i})_{i \in I}}$ be a family of modules over a von Neumann regular ring. It is shown that for the splitness of the canonical inclusion ${ \oplus _{i \in I}}{M_i} \subset \prod \nolimits _{i \in I} {{M_i}}$ it is necessary and sufficient that there be a finite subset $I’$ of $I$ such that the restricted sum ${ \oplus _{i \in I\backslash I’}}{M_i}$ is semisimple with finitely many homogeneous components, all simple summands being finite dimensional over their endomorphism rings. This yields a characterization of those families of injectives whose direct sum is again injective.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 251-254
- MSC: Primary 16A52; Secondary 16A30
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624908-5
- MathSciNet review: 624908