| Title:
|
Linear identities in graph algebras (English) |
| Author:
|
Pilitowska, Agata |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
11-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras. (English) |
| Keyword:
|
graph algebra |
| Keyword:
|
linear identity |
| Keyword:
|
entropic algebra |
| Keyword:
|
equational basis |
| Keyword:
|
lattice of subvarieties |
| Keyword:
|
power algebra of subsets |
| MSC:
|
03C05 |
| MSC:
|
03C13 |
| MSC:
|
08A05 |
| MSC:
|
08A40 |
| MSC:
|
08A62 |
| MSC:
|
08A99 |
| MSC:
|
08B15 |
| MSC:
|
08C10 |
| MSC:
|
17D99 |
| idZBL:
|
Zbl 1212.08004 |
| idMR:
|
MR2562800 |
| . |
| Date available:
|
2009-08-18T12:22:38Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133411 |
| . |
| Reference:
|
[1] Baker K.A., McNulty G.F., Werner H.: The finitely based varieties of graph algebras.Acta Sci. Math. (Szeged) 51 (1987), 3--15. Zbl 0629.08003, MR 0911554 |
| Reference:
|
[2] Bošnjak I., Madarász R.: On power structures.Algebra Discrete Math. 2 (2003), 14--35. Zbl 1063.08001, MR 2048654 |
| Reference:
|
[3] Brink C.: Power structures.Algebra Universalis 30 (1993), 177--216. Zbl 0787.08001, MR 1223628, 10.1007/BF01196091 |
| Reference:
|
[4] Davey B.A., Idziak P.H., Lampe W.A., McNulty G.F.: Dualizability and graph algebras.Discrete Math. 214 (2000), 145--172. Zbl 0945.08001, MR 1743633, 10.1016/S0012-365X(99)00225-3 |
| Reference:
|
[5] Grätzer G., Lakser H.: Identities for globals $($complex algebras$)$ of algebras.Colloq. Math. 56 (1988), 19--29. MR 0980508 |
| Reference:
|
[6] Grätzer G., Whitney S.: Infinitary varieties of structures closed under the formation of complex structures.Colloq. Math. 48 (1984), 485--488. MR 0750749 |
| Reference:
|
[7] McNulty G.F., Shallon C.: Inherently nonfinitely based finite algebras.R. Freese, O. Garcia (Eds.), Universal Algebra and Lattice Theory (Puebla, 1982), Lecture Notes in Mathematics, 1004, Springer, Berlin, 1983, pp. 205--231. Zbl 0513.08003, MR 0716184 |
| Reference:
|
[8] Shafaat A.: On varieties closed under the construction of power algebras.Bull. Austral. Math. Soc. 11 (1974), 213--218. Zbl 0295.08002, MR 0364055, 10.1017/S000497270004380X |
| Reference:
|
[9] Shallon C.R.: Nonfinitely based binary algebras derived from lattices.Ph.D. Thesis, University of California at Los Angeles, 1979. |
| . |
