TL;DR
This paper introduces two non-additive languages for geometry by extending the concept of commutative rings, offering new frameworks for geometric reasoning.
Contribution
It presents novel non-additive languages for geometry through simple generalizations of commutative rings, expanding the algebraic tools available.
Findings
Two non-additive geometric languages introduced
Generalizations of commutative rings demonstrated
Frameworks for new geometric reasoning established
Abstract
We give (two) non additive languages for geometry via simple generalisations of commutative rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Advanced Topics in Algebra