Inverse-Complete Semiring
Year: 2025
Type: article
Abstract: This paper introduces new algebraic structure inverse-complete semiring (ICS)that generalizes semirings by incorporating a novel treatment of zero and di-vision by zero (DBZ). Unlike conventional semirings, ICS introduces a non-absorbing zero that allows for the existence of multiplicative inverses for allelements, including zero. This paper provides a consistent algebraic foundationfor handling previously undefined operations, such as division by zero, and offerspotential applications in mathematical fields where singularities and undefinedbehavior arise.
Author: Mtskerashvili
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893101166
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