In calculus, an indefinite integral of a function $f$ is a differentiable function $F$ whose derivative is equal to $f$. In present paper, we generalize this notion of the indefinite integral from the ring of real functions to any ring. The main goal of the paper is to focus on the properties of such generalized integrals that are inherited from the well-known basic properties of indefinite integrals of real functions.

翻译：在微积分中,一个功能(f$)的无限组成部分是一种不同的功能(F$),其衍生物等于f美元。在本文件中,我们把从实际功能圈到任何功能圈的无限组成部分的概念概括为这个概念。本文件的主要目标是侧重于从已知的真实功能的无限组成部分的基本特性所继承的这种普遍组成部分的特性。