| Title:
|
Generalized deductive systems in subregular varieties (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
319-324 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An algebra ${\mathcal A}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text{Con}\,{\mathcal A}$ we have $\Theta = \Phi $ whenever $[g(a)]_{\Theta } = [g(a)]_{\Phi }$ for each $a\in A$. We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C\subseteq A$ is a class of some congruence on $\Theta $ containing $g(a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps). (English) |
| Keyword:
|
regular variety |
| Keyword:
|
subregular variety |
| Keyword:
|
deductive system |
| Keyword:
|
congruence class |
| Keyword:
|
difference system |
| MSC:
|
03B22 |
| MSC:
|
08A30 |
| MSC:
|
08B05 |
| idZBL:
|
Zbl 1051.08002 |
| idMR:
|
MR2012608 |
| DOI:
|
10.21136/MB.2003.134184 |
| . |
| Date available:
|
2009-09-24T22:10:12Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134184 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
