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arXiv · 2203.01086

$\mathcal{T}$-semiring pairs

Jaiung Jun·Kalina Mincheva·Louis Rowen
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Abstract

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.

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Jaiung Jun, Kalina Mincheva, Louis Rowen. 2022-08-07. $\mathcal{T}$-semiring pairs. https://arxiv.org/abs/2203.01086

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