TITLE:
Two-Dimensional Lattice-Ordered Algebras over ℝ-Revisit
AUTHORS:
Jingjing Ma
KEYWORDS:
Direct Product, -Algebra, Squares Positive, -Basis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.16 No.4,
April
30,
2026
ABSTRACT: In this paper, it is first pointed out that the enumeration of two-dimensional lattice-ordered real algebras provided by Birkhoff and Pierce is complete. Then we classify lattice-ordered algebra
F×F
over a totally ordered field
F
. Finally in section 4, we provide more information on the partially ordered rings in which every square is positive, especially a characterization of partially ordered fields in which every square is positive is given.