| Title:
|
Compatible Idempotent Terms in Universal Algebra (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Ledda, Antonio |
| Author:
|
Paoli, Francesco |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
35-51 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term $t(x)$) in every member of the given variety. Here, we try to give a unified account of this phenomenon. In particular, we investigate what happens when various congruence properties—like congruence distributivity, congruence permutability or congruence modularity—are not supposed to hold unrestrictedly in any $\mathbf {A}\in \mathcal {V}$, but only for congruence classes of values of the term operation $t^{\mathbf {A}}$. (English) |
| Keyword:
|
Congruence distributive variety |
| Keyword:
|
congruence modular variety |
| Keyword:
|
congruence permutable variety |
| Keyword:
|
idempotent endomorphism |
| MSC:
|
03C05 |
| MSC:
|
08A30 |
| MSC:
|
08B10 |
| idZBL:
|
Zbl 1315.08001 |
| idMR:
|
MR3331005 |
| . |
| Date available:
|
2014-12-16T14:56:52Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144038 |
| . |
| Reference:
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