Partially Ordered Algebraic SystemsOriginally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap in many individual and institutional libraries. |
Other editions - View all
Common terms and phrases
a₁ a₂ Abelian groups algebraic extension Amer Archimedean classes Archimedean f. o. Archimedean property assume b₁ BIRKHOFF carriers Chapter commutative field completes the proof condition contains convex subgroup Corollary cyclically ordered decomposition defined direct product divisors of zero dyadic fractions embedded equivalent exists extension F-ring f. o. field f. o. ring f. o. semigroup factor group finite number follows FUCHS full order group G groupoid Hence holds ideal identity implies intersection Journ L-ideals lattice lattice-ordered Lemma Let G lexicographic Math maximal element multiplication nilpotent normal subgroup o-epimorphism O-group o-isomorphic O-ring obtain order of G ordered groups ordinal sum orthogonal p. o. group p. o. groupoid p. o. set P₁ partial order positive cone positive elements Proc Proposition proved real numbers satisfies semi-continuous subgroup of G subsemigroup subset Theorem topology vector space whence x₁