English

$\mathcal{T}$-semiring pairs

Rings and Algebras 2022-08-09 v2 Commutative Algebra

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.

Keywords

Cite

@article{arxiv.2203.01086,
  title  = {$\mathcal{T}$-semiring pairs},
  author = {Jaiung Jun and Kalina Mincheva and Louis Rowen},
  journal= {arXiv preprint arXiv:2203.01086},
  year   = {2022}
}

Comments

23pp

R2 v1 2026-06-24T09:59:17.205Z