Linear identities in graph algebras

Agata Pilitowska

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 1, page 11-24
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

Pilitowska, Agata. "Linear identities in graph algebras." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 11-24. <http://eudml.org/doc/32477>.

@article{Pilitowska2009,
abstract = {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.},
author = {Pilitowska, Agata},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {graph algebra; linear identity; entropic algebra; equational basis; lattice of subvarieties; power algebra of subsets; graph algebra; linear identity; entropic algebra; equational basis; lattice of subvarieties; power algebra of subsets},
language = {eng},
number = {1},
pages = {11-24},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Linear identities in graph algebras},
url = {http://eudml.org/doc/32477},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Pilitowska, Agata
TI - Linear identities in graph algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 11
EP - 24
AB - 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.
LA - eng
KW - graph algebra; linear identity; entropic algebra; equational basis; lattice of subvarieties; power algebra of subsets; graph algebra; linear identity; entropic algebra; equational basis; lattice of subvarieties; power algebra of subsets
UR - http://eudml.org/doc/32477
ER -

References

top
  1. Baker K.A., McNulty G.F., Werner H., The finitely based varieties of graph algebras, Acta Sci. Math. (Szeged) 51 (1987), 3--15. (1987) Zbl0629.08003MR0911554
  2. Bošnjak I., Madarász R., On power structures, Algebra Discrete Math. 2 (2003), 14--35. (2003) Zbl1063.08001MR2048654
  3. Brink C., 10.1007/BF01196091, Algebra Universalis 30 (1993), 177--216. (1993) Zbl0787.08001MR1223628DOI10.1007/BF01196091
  4. Davey B.A., Idziak P.H., Lampe W.A., McNulty G.F., 10.1016/S0012-365X(99)00225-3, Discrete Math. 214 (2000), 145--172. (2000) Zbl0945.08001MR1743633DOI10.1016/S0012-365X(99)00225-3
  5. Grätzer G., Lakser H., Identities for globals ( complex algebras ) of algebras, Colloq. Math. 56 (1988), 19--29. (1988) MR0980508
  6. Grätzer G., Whitney S., Infinitary varieties of structures closed under the formation of complex structures, Colloq. Math. 48 (1984), 485--488. (1984) MR0750749
  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. Zbl0513.08003MR0716184
  8. Shafaat A., 10.1017/S000497270004380X, Bull. Austral. Math. Soc. 11 (1974), 213--218. (1974) Zbl0295.08002MR0364055DOI10.1017/S000497270004380X
  9. Shallon C.R., Nonfinitely based binary algebras derived from lattices, Ph.D. Thesis, University of California at Los Angeles, 1979. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.