Quasivarieties of pseudo-$MV$-algebras

O. A. Kuryleva

Altai State University

Abstract: Denote by $\varUpsilon_1$ the collection of quasivarieties of pseudo-$MV$-algebras; and by $\varUpsilon_2$, the collection of quasivarieties of lattice-ordered groups. With respect to the set-theoretic inclusion, $\varUpsilon_1$ and $\varUpsilon_2$ are lattices. We note some properties of $\varUpsilon_1$ and construct an injective mapping $\varphi$ of $\varUpsilon_2$ into $\varUpsilon_1$ such that $Z_1\subseteq Z_2\Leftrightarrow\varphi(Z_1)\subseteq\varphi(Z_2)$ for all $Z_1,Z_2\in\varUpsilon_2$.

Keywords: lattice-ordered group, pseudo-$MV$-algebra, quasivariety.

UDC: 512.54

Received: 29.05.2007

 English version: Siberian Mathematical Journal, 2008, 49:3, 452–456

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