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The Theory of Rings

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The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.

Author(s): Nathan Jacobson
Series: Mathematical Surveys and Monographs
Publisher: American Mathematical Society
Year: 1943

Language: English
Commentary: OCR, Front and Back Covers, Bookmarks, Pagination
Pages: 150

Chap 1 - GROUPS AND ENDOMORPHISMS 1
Chap 2 - VECTOR SPACES 17
Chap 3 - NON-COMMUTATIVE PRINCIPAL IDEAL DOMAINS 29
Chap 4 - STRUCTURE OF RINGS OF ENDOMORPHISMS AND OF ABSTRACT RINGS 54
Chap 5 - ALGEBRAS OVER A FIELD 88
Chap 6 - MULTIPLICATIVE IDEAL THEORY 118
BIBLIOGRAPHY 141
INDEX 149