A Course in Ring Theory (Chelsea Publications) - Tapa dura

American Mathematical Society

 
9780821836804: A Course in Ring Theory (Chelsea Publications)
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ISBN 10: 0821836803 ISBN 13: 9780821836804
Editorial: American Mathematical Society, 2004

Sinopsis

First published in 1991, this book contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. In particular, a number of major results are highlighted and proved. Part I, 'Projective Modules', begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderbum, Artinian and Noetherian rings, hereditary rings, Dedekind domains, etc.). This part concludes with an introduction and discussion of the concepts of the projective dimension.Part II, 'Polynomial Rings', studies these rings in a mildly noncommutative setting. Some of the results proved include the Hilbert Syzygy Theorem (in the commutative case) and the Hilbert Nullstellensatz (for almost commutative rings). Part III, 'Injective Modules', includes, in particular, various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings. The book contains numerous exercises and a list of suggested additional reading. It is suitable for graduate students and researchers interested in ring theory.

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Reseña del editor

First published in 1991, this book contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. In particular, a number of major results are highlighted and proved. The first part of the book, called "Projective Modules", begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderburn, Artinian and Noetherian rings, hereditary rings, Dedekind domains, etc.). This part concludes with an introduction and discussion of the concepts of the projective dimension. Part II, "Polynomial Rings", studies these rings in a mildly noncommutative setting. Some of the results proved include the Hilbert Syzygy Theorem (in the commutative case) and the Hilbert Nullstellensatz (for almost commutative rings). Part III, "Injective Modules", includes, in particular, various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings. The book contains numerous exercises and a list of suggested additional reading. It is suitable for graduate students and researchers interested in ring theory.

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Editorial
American Mathematical Society
Año de publicación
2004
Idioma
Inglés
ISBN 10 
0821836803
ISBN 13 
9780821836804
Encuadernación
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Número de páginas
306
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9780534137762: Course in Ring Theory (Wadsworth and Brooks/Cole Mathematics Series)

Edición Destacada

ISBN 10:  0534137768 ISBN 13:  9780534137762
Editorial: Brooks/Cole, 1998
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