$\mathcal {T}$-semiring pairs

Jun, Jaiung ; Mincheva, Kalina ; Rowen, Louis

Kybernetika, Tome 58 (2022) no. 5, pp. 733-759

Abstract (VO)

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.

Détail

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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