2004/02/01 by JESPER CARLSTRM · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Rings, Modules, and Algebras #Semiring #Axiom #Commutative ring #Mathematics #Commutative property #Ring (chemistry) #Noncommutative ring #Identity (music) #Pure mathematics #Division (mathematics) #Zero (linguistics) #Zero divisor #Element (criminal law) #Division ring #Algebra over a field #Geometry #Arithmetic #Physics #Law
paper · doi:10.1017/s0960129503004110
openalex publication_date 2004/02/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/05/17
We show how to extend any commutative ring (or semiring) so that division by any element, including 0, is, in a sense, possible. The resulting structure is called a wheel. Wheels are similar to rings, but of any wheel is a commutative ring (or semiring), and any commutative ring (or semiring) with identity can be described as such a subset of a wheel. The main goal of this paper is to show that the given axioms for wheels are natural, and to clarify how valid identities for wheels relate to valid identities for commutative rings and semirings.