Rings with involution as partially ordered Abelian groups

DOI10.1216/RMJ-1981-11-3-337zbMath0473.16013MaRDI QIDQ1158496

David E. Handelman

Publication date: 1981

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

positive conedivision ringstate spacering with involutionArtin-Schreier theorempartially ordered abelian groupsRiesz interpolation propertyself-adjoint elementsmatrix rings over Baer-ringsorder-completenessreal division *- algebrasemiprime Goldie ringtotal orderings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) General theory of topological algebras with involution (46K05) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Ordered fields (12J15) Division rings and semisimple Artin rings (16Kxx)

Related Items (19)

*-IDEALS AND FORMAL MORITA EQUIVALENCE OF *-ALGEBRAS ⋮ The extend centroid of C*-algebras ⋮ c-orderable division rings with involution ⋮ Noncommutative Positivstellensätze for pairs representation-vector ⋮ Finsler's lemma for matrix polynomials ⋮ Archimedean operator-theoretic Positivstellensätze ⋮ States and synaptic algebras ⋮ Synaptic algebras as models for quantum mechanics ⋮ A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra ⋮ Regular elements in generalized hermitian algebras ⋮ Maximal quadratic modules on \(*\)-rings. ⋮ Rickart C* algebras. II ⋮ ^*-Orderings on a ring with involution ⋮ Observables on synaptic algebras ⋮ Simple archimedean dimension groups ⋮ Dimension functions and traces on C*-algebras ⋮ Representation of partial *-orderings ⋮ On 𝑞-normal operators and the quantum complex plane ⋮ IN PRAISE OF ORDER UNITS

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