| Title:
|
Embedding sums of cancellative modes into semimodules (English) |
| Author:
|
Romanowska, Anna |
| Author:
|
Zamojska-Dzienio, Anna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
975-991 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice. (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:
|
08C15 |
| idZBL:
|
Zbl 1081.08003 |
| idMR:
|
MR2184378 |
| . |
| Date available:
|
2009-09-24T11:29:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128039 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] J. Kuras: Application of Agassiz Systems to Represantation of Sums of Equationally Defined Classes of Algebras.PhD. Thesis, M. Kopernik University, Toruń, 1985. (Polish) |
| 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] A. B. Romanowska and J. D. H. Smith: 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, J. M. Abe, S. Tanaka (eds.), IOS Press, Amsterdam, 2001, pp. 127–139. MR 1896671 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[13] A. B. Romanowska and A. Zamojska-Dzienio: Embedding semilattice sums of cancellative modes into semimodules.Contributions to General Algebra 13 (2001), 295–303. MR 1854593 |
| Reference:
|
[14] J. D. H. Smith: Modes and modals.Discuss. Math. Algebra & Stochastic Methods 19 (1999), 9–40. Zbl 0937.08006, MR 1701734 |
| . |
