Some trends in lattice-ordered groups and rings. (English) Zbl 0838.06015
Baker, K. A. (ed.) et al., Lattice theory and its applications. In celebration of Garrett Birkhoff’s 80th birthday. Lemgo: Heldermann Verlag. Res. Expo. Math. 23, 131-161 (1995).
Some aspects of the theory of lattice-ordered groups and rings are considered in this survey. The author considers this theory in a more general mathematical context and stresses its relations to some other fields of mathematics.
The paper includes the following issues: the roots, the birth, two highlights, \(\ell\)-group polynomials and free \(\ell\)-groups, real semialgebraic geometry and lattice-ordered rings.
The article contains interesting historical facts and several open questions and problems. The bibliography consists of 81 items.
For the entire collection see [Zbl 0824.00024].
The paper includes the following issues: the roots, the birth, two highlights, \(\ell\)-group polynomials and free \(\ell\)-groups, real semialgebraic geometry and lattice-ordered rings.
The article contains interesting historical facts and several open questions and problems. The bibliography consists of 81 items.
For the entire collection see [Zbl 0824.00024].
Reviewer: S.A.Gurchenkov (Rubtsovsk)
MSC:
| 06F15 | Ordered groups |
| 06F20 | Ordered abelian groups, Riesz groups, ordered linear spaces |
| 06F25 | Ordered rings, algebras, modules |
| 06-02 | Research exposition (monographs, survey articles) pertaining to ordered structures |
| 06-03 | History of ordered structures |
