| Title:
|
On modular elements of the lattice of semigroup varieties (English) |
| Author:
|
Vernikov, Boris M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
595-606 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A semigroup variety is called {\it modular\/} if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity $u=v$ is called {\it substitutive\/} if the words $u$ and $v$ depend on the same letters and $v$ may be obtained from $u$ by renaming of letters.) We completely determine all commutative modular varieties and obtain an essential information about modular varieties satisfying a permutable identity. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
variety |
| Keyword:
|
nil-variety |
| Keyword:
|
0-reduced identity |
| Keyword:
|
substitutive identity |
| Keyword:
|
permutable identity |
| Keyword:
|
lattice of subvarieties |
| Keyword:
|
modular element of a lattice |
| Keyword:
|
upper-modular element of a lattice |
| MSC:
|
08B15 |
| MSC:
|
20M07 |
| idZBL:
|
Zbl 1174.20324 |
| idMR:
|
MR2375161 |
| . |
| Date available:
|
2009-05-05T17:05:00Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119683 |
| . |
| 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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| Reference:
|
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| . |
