Kybernetika 58 no. 5, 733-759, 2022

$\mathcal{T}$-semiring pairs

Jaiung Jun, Kalina Mincheva and Louis RowenDOI: 10.14736/kyb-2022-5-0733

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:

congruence, module, semiring, pair, system, triple, shallow, algebraic, integral, affine, Ore, negation map

Classification:

08A30, 08A72, 18A05, 16Y60, 14T10, 12K10, 13C60, 18E05, 18C10, 08A05, 20N20

paper.pdf

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