Bases for the k-normalizations of varieties of bands

• Autorzy: Cheng V. , Wismath S.
• Języki publikacji: EN

Abstrakty

EN

The usual depth measurement on terms of a fixed type type r assigns to each term a non-negative integer called its depth. For k > l, an identity s ~ t of type r is said to be k-normal (with respect to the depth measurement) if either s = t or both s and t have depth > k. Taking k=1 gives the well-known property of normality of identities. A variety is called k-normal (with respect to the depth measurement) if all its identities are k-normal. For any variety V, there is a least k-normal variety Nk(V) containing V, the variety determined by the set of all k-normal identities of V. In this paper we produce for every subvariety V of the variety B of bands (idempotent semigroups) a finite equational basis for Nk(V), for k > 1.

Słowa kluczowe

EN

k-normal identities; bands; finite equational basis

PL

diagramy; równania skończone

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 4
• Strony: 775--787
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Cheng V.

autor

Wismath S.

• Math/CS. Dept. University of Lethbridge 4401 University Drive Lethbridge, AB,. Canada TIK-3M4,

Bibliografia

• [1] P. A. Birjukov, Varirties of idempotent semigroups, Algebra i Logika 9 (1970), 255-273 (in Russian).
• [2] K. Denecke and S. L. Wismath, A Characterization of k-normal varieties, Algebra Universalis 51 (2004), no. 4, 395-409.
• [3] K. Denecke and S. L. Wismath, Valuations of terms, Algebra Universalis 50 (2003), no. 1, 107-128.
• [4] C. Fennemore, All varieties of bands I, II, Math. Nachr. 48 (1971), 237-252, 253-262.
• [5] J. A. Gerhard, The lattice of equational classes of idempotent semigroups, J. Algebra 15 (1970), 195-224.
• [6] J. A. Gerhard and M. Petrich, Varieties of bands revisited. Proc. London Math. Soc. 58 (1989), no. 3, 323-350.
• [7] E. Graczyńska, On normal and regular identities, Algebra Universalis 27 (1990), no. 3, 387-397.
• [8] C. Masse, H. Wang and S. L. Wismath, A basis for the k-normalization of semigroups, preprint, 2006.