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Free products of $$\ell$$-groups. (English. Russian original) Zbl 0577.06014
Algebra Logic 23, 336-346 (1984); translation from Algebra Logika 23, No. 5, 493-511 (1984).
From the author’s introduction: The article contains the following main results: It is proved that sublattices of free products in varieties of nilpotent $$\ell$$-groups generated by the free factors are free products of $$D_{\ell}$$-lattices (Theorem 1); it is proved that the free products of finitely generated $$\ell$$-groups in arbitrary varieties of $$\ell$$- groups contained in the variety of $$\ell$$-groups with subnormal jumps are irreducible into an $$\ell$$-direct product (Theorem 2); it is proved that the lattice of quasivarieties of $$\ell$$-groups is not modular (Theorem 3); examples of varieties of associative lattice-ordered rings having no finite basis of identities are constructed (Propositions 1 and 2).
Reviewer: F.Šik

MSC:
 06F15 Ordered groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F18 Nilpotent groups 20F60 Ordered groups (group-theoretic aspects) 20E10 Quasivarieties and varieties of groups 06B20 Varieties of lattices 08B15 Lattices of varieties 08C15 Quasivarieties
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