All subvarieties of $\mathscr{L}_{pq}$ have finite bases of identities

N. N. Naritsyn

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: We consider the varieties of lattice ordered groups with the identity of commutation of the $n$-th powers of elements. We establish that every such $\ell$-variety with $n=pq$, where $p$ and $q$ are distinct prime numbers, has a finite basis of identities.

Keywords: variety, lattice ordered group, identity, finite basis.

UDC: 512.545

Received: 16.04.2002
Revised: 18.11.2002

 English version: Siberian Mathematical Journal, 2003, 44:3, 500–510

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