TL;DR
This paper generalizes the concept of indefinite integrals from real functions to arbitrary rings, exploring how their fundamental properties extend beyond classical calculus.
Contribution
It introduces a new framework for indefinite integrals within ring theory, broadening the scope of integral calculus to algebraic structures.
Findings
Properties of generalized integrals mirror classical indefinite integrals
Extension of calculus concepts to algebraic structures
Foundational groundwork for further algebraic integration studies
Abstract
In calculus, an indefinite integral of a function is a differentiable function whose derivative is equal to . 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.
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