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$\\textbf{Theorem 1.4.}$ 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 $A$, 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over strongly semiprime ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Askar Tuganbaev","submitted_at":"2017-01-25T00:41:58Z","abstract_excerpt":"$\\textbf{Theorem 1.3.}$ 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 $A$, 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