This paper is a continuation of ideas presented by Bagirmaz (Appl Algebra Eng Commun Comput 30(4):285–297, 2019). Indeed, we introduce the notion of near approximations in a ring, which is an extended notion of a rough approximations in a ring. Then we define lower and upper near subrings based on ideals in a ring and give some properties of such subrings. Furthermore, we obtain a comparison between these types of approximations and the approximations introduced by Davvaz (Inf Sci 176:2417–2437, 2006).

中文翻译：

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环中的近似值

本文是 Bagirmaz 提出的想法的延续（Appl Algebra Eng Commun Comput 30(4):285–297, 2019）。事实上，我们引入了环中近似近似的概念，这是环中粗略近似的扩展概念。然后我们根据环中的理想定义下近子环和上近子环，并给出这些子环的一些性质。此外，我们获得了这些类型的近似值与 Davvaz 引入的近似值之间的比较（Inf Sci 176:2417–2437, 2006）。