| Title:
|
Medial modes and rectangular algebras (English) |
| Author:
|
Zamojska-Dzienio, Anna |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
21-34 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Medial modes, a natural generalization of normal bands, were investigated by P\l onka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results of A. Romanowska, J.D.H. Smith and A. Zamojska-Dzienio. (English) |
| Keyword:
|
modes (idempotent and entropic algebras) |
| Keyword:
|
cancellative modes |
| Keyword:
|
sums of algebras |
| Keyword:
|
embeddings |
| Keyword:
|
semimodules over semirings |
| Keyword:
|
idempotent subreducts of semimodules |
| MSC:
|
03C05 |
| MSC:
|
08A05 |
| MSC:
|
08A40 |
| MSC:
|
08C15 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 1138.08001 |
| idMR:
|
MR2223964 |
| . |
| Date available:
|
2009-05-05T16:55:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119571 |
| . |
| 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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| Reference:
|
[10] Romanowska A.B., Smith J.D.H.: Embedding sums of cancellative modes into functorial sums of affine spaces.in Unsolved Problems on Mathematics for the 21st Century, a Tribute to Kiyoshi Iseki's 80th Birthday (eds. J.M. Abe and S. Tanaka), IOS Press, Amsterdam, 2001, pp.127-139. Zbl 0989.08001, MR 1896671 |
| 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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| . |
