Quotient gamma nearness rings

The aim of this paper is to defined the quotient gamma nearness rings and to examine its properties. We generalize an important theorem for quotient gamma nearness rings. More clearly, we prove the following theorem: Let \(M\ne \left\{ 0_{M}\right\} \) $M\ne \left\{0_M\right\}$ be a commutative \(\Gamma \) $\mathrm{\Gamma }$ -nearness ring such that \(N_{r}(B)^{*}(N_{r}(B)^{*}M)=N_{r}(B)^{*}M\) $N_r(B)_{}^{\ast }(N_r(B)_{}^{\ast }M)=N_r(B)_{}^{\ast }M$ , P be a \( \Gamma \) $\mathrm{\Gamma }$ -nearness ideal of M such that \(N_{r}(B)^{*}(N_{r}(B)^{*}P)=N_{r}(B)^{*}P\) $N_r(B)_{}^{\ast }(N_r(B)_{}^{\ast }P)=N_r(B)_{}^{\ast }P$ , and \(\sim _{B_{r}}\) ${\sim }_{B_r}$ be a congruence indiscernibility relation on M. Then, P is a prime \(\Gamma \) $\mathrm{\Gamma }$ -nearness ideal if and only if M/P is a \(\Gamma \) $\mathrm{\Gamma }$ -nearness integral domain.