From rings to minimal Hv-fields

ON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...

Witt rings of quadratically presentable fields

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...

Introduction to Groups, Rings and Fields

Addition: for each pair of real numbers a and b there exists a unique real number a + b such that • + is a commutative and associative operation; • there exists in R a zero, 0, for addition: a+ 0 = 0 + a = a for all a ∈ R; • for each a ∈ R there exists an additive inverse −a ∈ R such that a+(−a) = (−a)+a = 0. Multiplication: for each pair of real numbers a and b there exists a unique real numbe...

Ordered Rings and Fields

Minimal Cost WDM SONET Rings

Minimal cost networks are presented when SONET UPSR and BLSR networks are deployed over a WDM fiber ring. The primary cost is the number of SONET ADMs, and a secondary cost is the number of wavelengths. The networks have been designed assuming a nonstatistical traffic model, and guarantees no blocking of traffic. Three network architectures are given that have low ADM costs. It is shown that ne...