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.
| Original language | English |
|---|---|
| Pages (from-to) | 733-759 |
| Number of pages | 27 |
| Journal | Kybernetika |
| Volume | 58 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 Institute of Information Theory and Automation of The Czech Academy of Sciences. All rights reserved.
Funding
The research of the second author is sponsored by Louisiana Board of Regents Targeted Enhancement Grant 090ENH-21. The research of the third author was supported by the ISF grant 1994/20.
| Funders | Funder number |
|---|---|
| Iowa Science Foundation | 1994/20 |
Keywords
- Ore
- affine
- algebraic
- congruence
- integral
- module
- negation map
- pair
- semiring
- shallow
- system
- triple