I've been reading Pete Clark's notes on commutative algebra, and I especially liked section 17 on valuation rings, and ordered groups in particular.

I'm looking for more introductory material regarding the ordering of groups, monoids and vectorspaces. Could anyone suggest something?

I'm interested in printed works as well as online notes and courses. I read some of this book online and it seems good ,but I want to see if anyone has a more informed opinion.

  • $\begingroup$ Have you tried to enter "ordered groups" into google? $\endgroup$ May 19, 2013 at 9:11
  • $\begingroup$ @Martin: Yes, it finds more results than I could possibly ever read, which is why I'm soliciting reviews. $\endgroup$
    – Xodarap
    May 19, 2013 at 15:03
  • $\begingroup$ Try also the following books: (1) "Partially Ordered Algebraic Systems" by Laszlo Fuchs; (2) "Lattice-Ordered Rings and Modules" by Steinberg. $\endgroup$ Mar 14, 2021 at 4:17
  • $\begingroup$ Try also "Ordered Groups and Topology" by Clay and Rolfsen $\endgroup$ Mar 14, 2021 at 4:23

1 Answer 1


Mathscinet gives a favourable review of the book you mention, namely Partially Ordered Groups by A. M. W. Glass. The review says that it `will surely be an instant classic', and it has apparently been cited 78 times. It concludes saying that the book

will get the reader to the forefront of research in the field and would be suitable texts for students in modern algebra, group theory, or ordered structures.

As for other resources, Dale Rolfsen has notes on Ordered Groups and Topology: see http://www.math.ubc.ca/~rolfsen/papers/luminynotes/lum.pdf.


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