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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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