| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2023-01-23T16:31:51Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151301 |
| . |
| Reference:
|
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