Modules over strongly semiprime rings
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Askar A. Tuganbaev
Abstract
For a ring A, the following conditions are equivalent.
A is a right strongly semiprime ring.
Every right A-module which is injective with respect to some essential right ideal of the ring A, is an injective module.
Every quasi-injective right A-module which is injective with respect to some essential right ideal of the ring A is an injective module.
Note: Originally published in Diskretnaya Matematika (2017) 30, №3, 129–135 (in Russian).
Funding
The study is supported by Russian Science Foundation (project no. 16-11-10013)
Acknowledgement
The author thanks I. B. Kozhukhov for useful remarks.
References
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Articles in the same Issue
- Frontmatter
- Generalization of one method of a filter generator key recovery
- Boolean functions as points on the hypersphere in the Euclidean space
- Artinian bimodule with quasi-Frobenius bimodule of translations
- Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors
- On some properties of vector functions of Boolean algebra
- Modules over strongly semiprime rings
Articles in the same Issue
- Frontmatter
- Generalization of one method of a filter generator key recovery
- Boolean functions as points on the hypersphere in the Euclidean space
- Artinian bimodule with quasi-Frobenius bimodule of translations
- Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors
- On some properties of vector functions of Boolean algebra
- Modules over strongly semiprime rings
