International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 75-80
Strong amalgamations of lattice ordered groups and modules
1Department of Mathematics and Computer Science, Texas Woman's University, Denton 76204, Texas, USA
2Department of Mathematics, Oklahoma State University, Stillwater 74078, Oklahoma, USA
Received 25 September 1990; Revised 21 January 1992
Copyright © 1993 Mona Cherri and Wayne B. Powell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that every variety of representable lattice ordered groups fails the strong
amalgamation property. The same result holds for the variety of -modules over an -ring.
However, strong amalgamations do occur for abelian lattice ordered groups or -modules when the
embeddings are convex.