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Generalized discrete l-groups

Published online by Cambridge University Press:  09 April 2009

Joe L. Mott
Joe L. Mott
Affiliation:
Florida State UniversityTallahassee, Florida 32306, U.S.A.
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Let G be an abelian lattice ordered group (an l-group). If G is, in fact, totally ordered, we say that G is an 0–group. A subgroup and a sublattice of G is an l-subgroup. A subgroup C of G is called convex if 0 ≦ g ≦ c ∈ C and g ∈ G imply g ∈ C, C is an l-ideal if C is a convex l-subgroup of G. If C is an l-ideal of G, then G/C is also an l-group under the canonical ordering inherited from G. If, in fact, G/C is an 0–group, then C is said to be a prime subgroup of G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 281 - 289
Copyright
Copyright © Australian Mathematical Society 1975

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