Topological Rings Satisfying Compactness ConditionsSpringer Science & Business Media, 31.12.2002 - 327 Seiten Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts. |
Inhalt
III | 1 |
IV | 5 |
V | 8 |
VI | 11 |
VII | 15 |
VIII | 19 |
IX | 28 |
X | 31 |
XXIX | 147 |
XXX | 153 |
XXXI | 168 |
XXXII | 170 |
XXXIII | 175 |
XXXIV | 177 |
XXXV | 184 |
XXXVI | 198 |
XI | 34 |
XII | 35 |
XIII | 38 |
XIV | 45 |
XV | 59 |
XVI | 71 |
XVII | 75 |
XVIII | 77 |
XIX | 78 |
XX | 80 |
XXII | 83 |
XXIII | 90 |
XXIV | 93 |
XXV | 94 |
XXVI | 113 |
XXVII | 124 |
XXVIII | 143 |
XXXVII | 201 |
XXXVIII | 207 |
XXXIX | 226 |
XL | 239 |
XLI | 247 |
XLII | 256 |
XLIII | 261 |
XLIV | 266 |
XLV | 268 |
XLVI | 281 |
XLVII | 285 |
XLVIII | 299 |
XLIX | 301 |
L | 305 |
315 | |
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Häufige Begriffe und Wortgruppen
A₁ affirm algebraic Assume the contrary base consisting canonical homomorphism Cauchy filter closed subgroup cofinite compact group compact right topological compact topology Consider contains continuous homomorphism contradiction COROLLARY Denote dense direct sum discrete division ring exists a neighborhood filter base finite subset follows fundamental system group G group topology hence idempotent Jacobson radical k₁ LCA group left ideal Lemma Let G linearly compact locally compact ring locally topologically nilpotent mapping Matem module natural number neighborhood of zero nilpotent ideal nilring non-discrete non-zero Obviously open ideal open subgroup PROOF proved quotient ring R-module right ideal right topological ring ring topology ring with identity semisimple submodule subring subspace system of neighborhoods THEOREM topological Abelian group topological direct topological group topological product topological ring topological space topologically isomorphic topologically locally finite totally bounded totally disconnected two-sided ideal U₁ V₁ W₁