We consider algebras determined by all normal identities of basic algebras. For such algebras, we present a representation based on a q-lattice, i.e., the normalization of a lattice.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1146, author = {Miroslav Kola\v r\'\i k}, title = {Normalization of basic algebras}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {28}, year = {2008}, pages = {237-249}, zbl = {1195.06007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1146} }
Miroslav Kolařík. Normalization of basic algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 237-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1146/
[000] [1] I. Chajda, Lattices in quasiordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 31 (1992), 6-12. | Zbl 0773.06002
[001] [2] I. Chajda, Congruence properties of algebras in nilpotent shifts of varieties, pp. 35-46 in: General Algebra and Discrete Mathematics (K. Denecke, O. Lüders, eds.), Heldermann, Berlin 1995. | Zbl 0821.08009
[002] [3] I. Chajda, Normally presentable varieties, Algebra Universalis 34 (1995), 327-335.
[003] [4] I. Chajda and E. Graczyńska, Algebras presented by normal identities, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 38 (1999), 49-58. | Zbl 0993.08002
[004] [5] I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis, DOI 10.1007/s00012-008-2086-9. | Zbl 1219.06013
[005] [6] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 2007, ISBN 978-3-88538-230-0.
[006] [7] I. Chajda, R. Halaš, J. Kühr and A. Vanžurová, Normalization of MV-algebras, Mathematica Bohemica 130 (2005), 283-300. | Zbl 1112.06012
[007] [8] I. Chajda and M. Kolařík, Independence of axiom system of basic algebras, Soft Computing, DOI 10.1007/s00500-008-0291-2. | Zbl 1178.06007
[008] [9] I. Mel'nik, Nilpotent shifts of varieties, Math. Notes 14 (1973), 692-696 (in Russian).