A general representation theorem for partially ordered commutative rings

2002 ◽  
Vol 242 (2) ◽  
pp. 217-225 ◽  
Author(s):  
Murray Marshall
Keyword(s):  
Representation Theorem ◽  
Commutative Rings ◽  
General Representation ◽  
Partially Ordered

scholarly journals A Representation Theorem for Archimedean Quadratic Modules on ∗-Rings

2009 ◽  
Vol 52 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Jakob Cimprič
Keyword(s):  
Algebraic Geometry ◽  
Representation Theory ◽  
Representation Theorem ◽  
Commutative Rings ◽  
Real Algebraic Geometry ◽  
New Approach ◽  
Noncommutative Version ◽  
Quadratic Modules ◽  
Rings With Involution ◽  
Associative Rings

AbstractWe present a new approach to noncommutative real algebraic geometry based on the representation theory of C*-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand–Naimark representation theorem for commutative C*-algebras. A noncommutative version of Gelfand–Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution.

scholarly journals Complex and distributional weights for sieved ultraspherical polynomials

1996 ◽  
Vol 19 (2) ◽  
pp. 229-242
Author(s):  
Jairo A. Charris ◽  
Felix H. Soriano
Keyword(s):  
Real Line ◽  
Representation Theorem ◽  
Contour Integral ◽  
General Representation ◽  
The Real ◽  
Ultraspherical Polynomials ◽  
Natural Range

Contour integral and distributional orthogonality of sieved ultraspherical polynomials are established for values of the parameters outside the natural range of orthogonality by positive measures on the real line. A general representation theorem for moment functionals is included.

Structure of Uninorms

1997 ◽  
Vol 05 (04) ◽  
pp. 411-427 ◽  
Author(s):  
János C. Fodor ◽  
Ronald R. Yager ◽  
Alexander Rybalov
Keyword(s):  
Representation Theorem ◽  
Unit Interval ◽  
Neutral Element ◽  
General Representation ◽  
Exhaustive Study

An exhaustive study of uninorm operators is established. These operators are generalizations of t-norms and t-conorms allowing the neutral element lying anywhere in the unit interval. It is shown that uninorms can be built up from t-norms and t-conorms by a construction similar to ordinal sums. De Morgan classes of uninorms are also described. Representability of uninorms is characterized and a general representation theorem is proved. Finally, pseudo-continuous uninorms are defined and completely classified.

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