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arXiv · 1701.07117

Modules over strongly semiprime ring

Askar Tuganbaev
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Abstract

$\textbf{Theorem 1.3.}$ For a given ring $A$ with right Goldie radical $G(A_A)$, the following conditions are equivalent. $\textbf{1)}$ 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. $\textbf{2)}$ $A/G(A_A)$ is a right strongly semiprime ring. $\textbf{Theorem 1.4.}$ For a given ring $A$, the following conditions are equivalent. $\textbf{1)}$ $A$ is a right strongly semiprime ring. $\textbf{2)}$ 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.

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Askar Tuganbaev. 2017-01-25. Modules over strongly semiprime ring. https://arxiv.org/abs/1701.07117

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