2017/01/25 by A. A. Tuganbaev, Tuganbaev, Askar
Mathematics · #16D #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1701.07117
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Theorem 1.3. For a given ring A with right Goldie radical G(AA), the following conditions are equivalent. 1) Every non-singular right A-module X which is is injective with respect to some essential right ideal of the ring A is an injective module. 2) A/G(AA) is a right strongly semiprime ring. Theorem 1.4. For a given ring A, the following conditions are equivalent. 1) A is a right strongly semiprime ring. 2) Every right A-module which is injective with respect to some essential right ideal of the ring A, is an injective module and A is right non-singular.