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Residue Structures

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arxiv 2403.09467 v2 pith:CHNCJI3F submitted 2024-03-14 math.RA

Louis H. Rowen This is my paper · ORCID
classification math.RA
keywords constructionresiduecategoricalproductsstructuresadditivealgebrasbroader
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abstract

We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of nonassociative algebras. The residue construction, treated formally, satisfies the Noether isomorphism theorems, and also is cast in a broader categorical setting which includes categorical products, sums, and tensor products.

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  1. Semirings

    math.RA 2026-02 conditional novelty 5.0 of 10

    Rowen consolidates the pair/surpassing-relation framework that extends classical algebra (roots, matrices, linear algebra, geometry) to semirings without cancellation, adding new root-factor theorems and a map of open...

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