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Title: $\mathcal {T}$-semiring pairs (English)
Author: Jun, Jaiung
Author: Mincheva, Kalina
Author: Rowen, Louis
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 58
Issue: 5
Year: 2022
Pages: 733-759
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: pair
Keyword: semiring
Keyword: system
Keyword: triple
Keyword: shallow
Keyword: algebraic
Keyword: integral
Keyword: affine
Keyword: Ore
Keyword: negation map
Keyword: congruence
Keyword: module
MSC: 08A05
MSC: 08A30
MSC: 08A72
MSC: 12K10
MSC: 13C60
MSC: 14T10
MSC: 16Y60
MSC: 18A05
MSC: 18C10
MSC: 18E05
MSC: 20N20
idZBL: Zbl 07655857
idMR: MR4538623
DOI: 10.14736/kyb-2022-5-0733
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Date available: 2023-01-23T16:31:51Z
Last updated: 2023-03-13
Stable URL: http://hdl.handle.net/10338.dmlcz/151301
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