Exercises in Classical Ring TheorySpringer-Verlag, 1995 - 287 pages |
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Page 16
... properties : ( 1 ) Every submodule N C M is a direct summand of M , ( 2 ) M is the sum of a family of simple submodules , or ( 3 ) M is the direct sum of a family of simple submodules . Here , a simple module means a nonzero R - module ...
... properties : ( 1 ) Every submodule N C M is a direct summand of M , ( 2 ) M is the sum of a family of simple submodules , or ( 3 ) M is the direct sum of a family of simple submodules . Here , a simple module means a nonzero R - module ...
Page 222
... properties , most of which are proved by " lifting " corresponding properties from the semisimple ring R / rad R. One of the most important properties of a semilocal ring R is that it has " left stable range 1. " This property has ...
... properties , most of which are proved by " lifting " corresponding properties from the semisimple ring R / rad R. One of the most important properties of a semilocal ring R is that it has " left stable range 1. " This property has ...
Page 257
... properties of semiprimary rings . In his seminal 1960 paper , H. Bass studied the classes of perfect and semiperfect rings as homological gen- eralizations of semiprimary rings , and obtained striking characterizations of these rings ...
... properties of semiprimary rings . In his seminal 1960 paper , H. Bass studied the classes of perfect and semiperfect rings as homological gen- eralizations of semiprimary rings , and obtained striking characterizations of these rings ...
Table des matières
2 Semisimplicity | 16 |
Jacobson Radical Theory 35 1981 | 35 |
6 Group rings and the Jsemisimplicity problem | 57 |
Droits d'auteur | |
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Expressions et termes fréquents
a₁ abelian artinian ring assume automorphism B₁ central idempotents char commutative ring conjugate consider constructed contradiction decomposition Dedekind-finite defined division ring domain element endomorphism equation Exercise exists fact finite group finite-dimensional follows group G hopfian idempotent identity implies indecomposable integer inverse irreducible isomorphism J-semisimple Jacobson radical k-algebra kG-module left ideal left primitive ring Lemma Let G linear local ring M₁ matrix maximal ideal maximal left ideal maximal subfield minimal left module multiplication Neumann regular ring nil ideal nilpotent ideal noetherian ring noncommutative nonzero polynomial prime ideal primitive idempotents primitive rings proof prove quasi-regular R-module R/rad rad kG representation resp right ideal right R-module ring theory semilocal ring semiprime semisimple ring show that rad simple left R-module simple ring soc(RR Solution stable range strongly regular subdirect product subgroup subring Theorem unit-regular zero