Displaying similar documents to “Characteristic of Rings. Prime Fields”

Super real closed rings

Marcus Tressl (2007)

Fundamenta Mathematicae

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A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed...

The First Isomorphism Theorem and Other Properties of Rings

Artur Korniłowicz, Christoph Schwarzweller (2014)

Formalized Mathematics

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Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial

A Unified approach to the Structure Theory of PI-Rings and GPI-Rings

Brešar, Matej (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60. We give short proofs, based only on basic properties of the extended centroid of a prime ring, of Martindale’s theorem on prime GPI-rings and (a strengthened version of) Posner’s theorem on prime PI-rings. * Supported by the Slovenian Research Agency (program No. P1-0288).