Geodesic
$\mathcal {T}$-semiring pairs
Kybernetika, Tome 58 (2022) no. 5, pp. 733-759.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.14736/kyb-2022-5-0733
Classification : 08A05, 08A30, 08A72, 12K10, 13C60, 14T10, 16Y60, 18A05, 18C10, 18E05, 20N20
Keywords: pair; semiring; system; triple; shallow; algebraic; integral; affine; Ore; negation map; congruence; module 
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Jun, Jaiung; Mincheva, Kalina; Rowen, Louis. $\mathcal {T}$-semiring pairs. Kybernetika, Tome 58 (2022) no. 5, pp. 733-759. doi : 10.14736/kyb-2022-5-0733. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-5-0733/

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