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ring which contains all invertible elements of its maximal right ring of quotients. $\\textbf{Theorem 1.5.}$ For a ring $A$ with right Goldie radical $G(A_A)$, the following conditions are equivalent. $\\textbf{1)}$ $A/G(A_A)$ is a semiprime right Goldie ring. $\\textbf{2)}$ 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non-singular rings and modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Askar Tuganbaev","submitted_at":"2017-01-25T00:39:11Z","abstract_excerpt":"$\\textbf{Theorem 1.2.}$ For a ring $A$, the following conditions are equivalent. $\\textbf{1)}$ $A$ is a right automorphism-invariant right non-singular ring. $\\textbf{2)}$ $A$ is a right automorphism-invariant regular ring. $\\textbf{3)}$ $A=S\\times T$, where $S$ is a right injective regular ring and $T$ is a strongly regular ring which contains all invertible elements of its maximal right ring of quotients. $\\textbf{Theorem 1.5.}$ For a ring $A$ with right Goldie radical $G(A_A)$, the following conditions are equivalent. $\\textbf{1)}$ $A/G(A_A)$ is a semiprime right Goldie ring. $\\textbf{2)}$ 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