| Title:
|
On reductive and distributive algebras (English) |
| Author:
|
Romanowska, Anna |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
617-629 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega$-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega$-algebras, and of right $n$-step reductive $\Omega$-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties. (English) |
| Keyword:
|
idempotent and distributive groupoids and algebras |
| Keyword:
|
Mal'cev products of varieties of algebras |
| Keyword:
|
independent varieties |
| MSC:
|
03C05 |
| MSC:
|
08A05 |
| MSC:
|
08B05 |
| MSC:
|
08C15 |
| idZBL:
|
Zbl 1010.08002 |
| idMR:
|
MR1756540 |
| . |
| Date available:
|
2009-01-08T18:55:59Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119118 |
| . |
| 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:
|
[PRR] Pilitowska A., Romanowska A., Roszkowska B.: Products of mode varieties and algebras of subalgebras.Math. Slovaca 46 (1996), 497-514. Zbl 0890.08003, MR 1451038 |
| Reference:
|
[RS] Romanowska A., Smith J.D.H.: Modal Theory.Heldermann Verlag, Berlin, 1985. Zbl 0553.08001, MR 0788695 |
| Reference:
|
[RT] Romanowska A., Traina S.: Algebraic quasi-orders and sums of algebras.Discuss. Math. Algebra Stochastic Methods 19 (1999), 239-263. Zbl 0949.08001, MR 1709970 |
| . |
