Krull dimension

by Gordon, Robert

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Title Statements

Full title :Krull dimension / [by] Robert Gordon and J.C. Robson.

Summary

This memoir is devoted to the study of Krull dimensions of modules over (not necessarily commutative) rings with identity. Although not all modules have a Krull dimension, Noetherian modules always do. There has been much interest in the Krull dimension of noncommutative Noetherian rings and their modules. In this memoir, as well as providing an exposition of much of what is known about Krull dimension, we study those rings and modules, not necessarily Noetherian, which have a Krull dimension. The results we obtain show that merely having a Krull dimension is a stringent condition with many Noetherian-like consequences. We expect these results, and the methods involved, to have applications to Noetherian and related rings.

Edition Statements

Publication Date:©1973.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, R.I
Language:eng
Publication Date:©1973.

The Physical Object

Description:ii, 78 pages : : illustrations ; : 26 cm.

Edition Identifiers

ISBN:0821818333, 9780821818336
oclc:ocm00622632
LC Classification:QA3
Dewey Decimal:512/.4

Introduction -- Preliminaries -- Critical modules -- Semiprime rings -- Localizing subcategories - Nilpotency -- Criticals over semiprime rings -- Prime ideals -- Gabriel's correspondence -- Polynomials -- Examples.

Subjects

Anneaux associatifs Anneaux commutatifs Anneaux noethériens Associative rings Commutative rings Krull-Ring Modules (Algebra) Modules (Algèbre) Noetherian rings