Exercises in Classical Ring TheorySpringer Science & Business Media, 29 juin 2013 - 288 pages Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual. |
À l'intérieur du livre
Résultats 1-5 sur 92
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... module theory ( e.g. , projectivity , injectivity , and flatness ) , category theory ( e.g. , equivalences and dualities ) , or rings of quotients ( e.g. , Ore rings and Goldie rings ) . A selection of ex- ercises in these areas will ...
... module theory ( e.g. , projectivity , injectivity , and flatness ) , category theory ( e.g. , equivalences and dualities ) , or rings of quotients ( e.g. , Ore rings and Goldie rings ) . A selection of ex- ercises in these areas will ...
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... module M , left R - module N direct sum of M and N tensor product of MR and RN group of R - homomorphisms from M to N ring of R - endomorphisms of M socle of M ( composition ) length of M MOM ( n times ) direct product of the rings { R } ...
... module M , left R - module N direct sum of M and N tensor product of MR and RN group of R - homomorphisms from M to N ring of R - endomorphisms of M socle of M ( composition ) length of M MOM ( n times ) direct product of the rings { R } ...
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... module left , right annihilators of the set S ( semi ) group ring of the ( semi ) group G over the ring k polynomial ring over k with ( commuting ) variables { x ; : i Є I } free ring over k generated by { x¿ : i € I } skew polynomial ...
... module left , right annihilators of the set S ( semi ) group ring of the ( semi ) group G over the ring k polynomial ring over k with ( commuting ) variables { x ; : i Є I } free ring over k generated by { x¿ : i € I } skew polynomial ...
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... module , or on 1 - sided or 2 - sided ideals of a ring . Some of the exercises in this section lie at the foundations of noncom- mutative ring theory , and will be used freely in all later exercises . These include , for instance , the ...
... module , or on 1 - sided or 2 - sided ideals of a ring . Some of the exercises in this section lie at the foundations of noncom- mutative ring theory , and will be used freely in all later exercises . These include , for instance , the ...
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... module M is said to be hopfian ( after the topologist H. Hopf ) if any surjective R - endomorphism of M is an automorphism . ( 1 ) Show that any noetherian module M is hopfian . ( 2 ) Show that the left regular module RR is hopfian iff ...
... module M is said to be hopfian ( after the topologist H. Hopf ) if any surjective R - endomorphism of M is an automorphism . ( 1 ) Show that any noetherian module M is hopfian . ( 2 ) Show that the left regular module RR is hopfian iff ...
Table des matières
1 | |
16 | |
Jacobson Radical Theory 4 The Jacobson radical 123535 | 35 |
5 Jacobson radical under change of rings | 52 |
Introduction to Representation Theory 689 | 69 |
Linear groups | 98 |
Prime and Primitive Rings 103 | 102 |
11 Structure of primitive rings the Density Theorem | 119 |
Introduction to Division Rings | 151 |
15 Tensor products and maximal subfields | 176 |
Ordered Structures in Rings | 191 |
Local Rings Semilocal Rings | 211 |
21 The theory of idempotents | 229 |
22 Central idempotents and block decompositions | 251 |
24 Homological characterizations of perfect | 265 |
Subject Index | 281 |
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Expressions et termes fréquents
a₁ abelian artinian ring assume automorphism B₁ central idempotents char commutative ring conjugate 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 matrix maximal ideal maximal left ideal maximal subfield minimal left Mn(R 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