| Title:
|
On free modes (English) |
| Author:
|
Stronkowski, Michał Marek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
561-568 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a theorem describing the equational theory of all modes of a fixed type. We use this result to show that a free mode with at least one basic operation of arity at least three, over a set of cardinality at least two, does not satisfy identities selected by 'A. Szendrei in {\it Identities satisfied by convex linear forms\/}, Algebra Universalis {\bf 12} (1981), 103--122, that hold in any subreduct of a semimodule over a commutative semiring. This gives a negative answer to the question raised by A. Romanowska: Is it true that each mode is a subreduct of some semimodule over a commutative semiring? (English) |
| Keyword:
|
modes |
| Keyword:
|
Szendrei modes |
| Keyword:
|
subreducts |
| Keyword:
|
semimodules |
| Keyword:
|
equational theory |
| MSC:
|
03C05 |
| MSC:
|
03F07 |
| MSC:
|
08B05 |
| MSC:
|
08B20 |
| idZBL:
|
Zbl 1150.08304 |
| idMR:
|
MR2337411 |
| . |
| Date available:
|
2009-05-05T16:59:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119617 |
| . |
| Reference:
|
[1] Burris S., Sankappanavar H.P.: A Course in Universal Algebra.Graduate Texts in Mathematics 78, Springer, New York-Berlin, 1981; http://www.math.uwaterloo.ca/$^\sim $snburris/htdocs/ualg.html. Zbl 0478.08001, MR 0648287 |
| Reference:
|
[2] Dojer N.: Clones of modes.Contributions to General Algebra 16 (2005), 75-84. Zbl 1089.08004, MR 2166947 |
| Reference:
|
[3] Golan J.S.: The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science.Longman Scientific & Technical, Harlow, 1992. Zbl 0780.16036, MR 1163371 |
| Reference:
|
[4] Ježek J., Kepka T.: Medial Groupoids.Rozpravy ČSAV 93/2, Academia, Praha, 1983. MR 0734873 |
| Reference:
|
[5] Ježek J., Kepka T.: Linear equational theories and semimodule representations.Internat. J. Algebra Comput. 8 (1998), 599-615. MR 1675018 |
| Reference:
|
[6] Romanowska A.B.: Semi-affine modes and modals.Sci. Math. Jpn. 61 (2005), 159-194. Zbl 1067.08001, MR 2111551 |
| Reference:
|
[7] Romanowska A.B., Smith J.D.H.: Modes.World Scientific, Singapore, 2002. Zbl 1060.08009, MR 1932199 |
| Reference:
|
[8] Szendrei À.: Identities satisfied by convex linear forms.Algebra Universalis 12 (1981), 103-122. Zbl 0458.08006, MR 0608653 |
| . |
