A Large Class of Small Varieties of Lattice-Ordered Groups

DOI10.2307/2040312zbMath0312.06010OpenAlexW4255607889MaRDI QIDQ4071287

E. Scrimger

Publication date: 1975

Full work available at URL: https://doi.org/10.2307/2040312

Mathematics Subject Classification ID

Ordered groups (06F15) Varieties (08B99)

Related Items (29)

Varieties of lattice-ordered groups in which prime powers commute ⋮ Quasi-varieties of solvable lattice-ordered groups ⋮ A very large class of small varieties of lattice-ordered groups¹ ⋮ Metabelian varieties of \(\ell\)-groups which contain no non-abelian o- groups ⋮ The failure of the amalgamation property for representable varieties of l-groups ⋮ The Word Problem for Free Lattice-Ordered Groups (and Some Other Free Algebras) ⋮ The structure of \(\ell\)-group varieties ⋮ Suprema of classes of generalized Scrimger varieties of lattice ordered groups ⋮ A variety of lattice-ordered groups containing all representable covers of the abelian variety ⋮ The lex property of varieties of lattice ordered groups ⋮ Free products of lattice ordered groups ⋮ Nilpotent lattice-ordered groups ⋮ Coverings in the lattice of quasivarieties of \(l\)-groups ⋮ Varieties of lattice-ordered groups ⋮ Solvable covers of the Boolean variety of unital \(\ell \)-groups ⋮ Special-valued \(l\)-groups and Abelian covers ⋮ Above and Below Subgroups of a Lattice-Ordered Group ⋮ Cyclic extensions of the Medvedev ordered groups ⋮ Varieties of lattice ordered groups that contain no non-Abelian o-groups are solvable ⋮ Intrinsic metrics for lattice ordered groups ⋮ On the theory of varieties of lattice ordered groups ⋮ Minimal varieties of l-groups ⋮ Ordered groups ⋮ On the Scrimger varieties of lattice-ordered groups ⋮ On reversing the order of a lattice ordered group ⋮ Varieties of \(\ell\)-groups with the identity \([x^ p,y^ p=e\) have finite bases] ⋮ On coverings in the lattice of \(\ell\)-varieties ⋮ Meet-irreducible varieties of lattice-ordered groups ⋮ Connected topological lattice-ordered groups

Cites Work

• Wreath products of ordered permutation groups
• The lattice-ordered group of automorphisms of an ordered set
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