Forcing, arithmetic, division rings

Triangulaizability of Algebras Over Division Rings

Arithmetic of Circular Rings

Circular arithmetic, introduced by I. Gargantini and P. Henrici [2J as an extension of the complex arithmetic, provided the formulati­ on of methods for solving some problems of computational complex anal­ ysis (e. g. tl:e inclusion of the polynomial complex zeros [2J, [3J, cir­ cular approximation of the closed regions in the complex plane [IJ, [4J , ~J, [8J, the evaluations of complex functio...

Arithmetic Convolution Rings

Arithmetic convolution rings provide a general and unified treatment of many rings that have been called arithmetic; the best known examples are rings of complex valued functions with domain in the set of non-negative integers and multiplication the Cauchy product or the Dirichlet product. The emphasis here is on factorization and related properties of such rings which necessitates prior result...

Forcing Axioms and Cardinal Arithmetic

We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial principles which follow from strong forcing axioms: stationary set reflection, Moore’s Mapping Reflection Principle MRP and the P-ideal dichotomy introduced by Abraham and Todorčević which play the key rol...

Planar Division Neo-rings

Introduction. The notion of a division ring can be generalized to give a system whose addition is not necessarily associative, but which retains the property of coordinatizing an affine plane. Such a system will be called a planar division neo-ring (PDNR); examples of (infinite) PDNRs which are not division rings are known. If (R, +, •) is a finite power-associative PDNR, then (R, +) is shown t...