Strong amalgamations of lattice ordered groups and modules. (English) Zbl 0771.06008

Cherri, Mona; Powell, Wayne B.

Int. J. Math. Math. Sci. 16, No. 1, 75-80 (1993).

The authors consider two variations of the amalgamation property (AP and StAP) for classes of lattice-ordered groups and lattice-ordered modules. In Theorem 2 it is proved that each class of representable \(\ell\)-groups containing \(Z\) (the integers) and closed with respect to the formation of \(\ell\)-subgroups and direct products fails the StAP (strong amalgamation property). Theorem 3 states a similar result for a class of \(f\)-modules containing the ring \(S\) and closed with respect to the formation of \(\ell\)-submodules and direct products. In the last part of the paper the authors investigate the possibility of amalgamating two \(\ell\)-groups with a common convex \(\ell\)-subgroup. It is proved (Theorem 4) that it is possible in the variety of abelian \(\ell\)-groups and in the variety of lattice ordered modules generated by the totally ordered modules (even if the amalgamation is required to be strong).

Reviewer: K.Hałkowska (Opole)

MSC:

06F15	Ordered groups
06F25	Ordered rings, algebras, modules
08B25	Products, amalgamated products, and other kinds of limits and colimits

Keywords:

strong amalgamation property; amalgamation property; lattice-ordered groups; lattice-ordered modules; \(f\)-modules