𝒯 -semiring pairs

Jaiung Jun; Kalina Mincheva; Louis Rowen

Kybernetika (2022)

  • Volume: 58, Issue: 5, page 733-759
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Jun, Jaiung, Mincheva, Kalina, and Rowen, Louis. "$\mathcal {T}$-semiring pairs." Kybernetika 58.5 (2022): 733-759. <http://eudml.org/doc/299476>.

@article{Jun2022,
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.},
author = {Jun, Jaiung, Mincheva, Kalina, Rowen, Louis},
journal = {Kybernetika},
keywords = {pair; semiring; system; triple; shallow; algebraic; integral; affine; Ore; negation map; congruence; module},
language = {eng},
number = {5},
pages = {733-759},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$\mathcal \{T\}$-semiring pairs},
url = {http://eudml.org/doc/299476},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Jun, Jaiung
AU - Mincheva, Kalina
AU - Rowen, Louis
TI - $\mathcal {T}$-semiring pairs
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 5
SP - 733
EP - 759
AB - 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.
LA - eng
KW - pair; semiring; system; triple; shallow; algebraic; integral; affine; Ore; negation map; congruence; module
UR - http://eudml.org/doc/299476
ER -

References

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