Primary Decomposition of Modules

Primary Decomposition of Modules


Sudhir R. Ghorpade and Jugal K. Verma

Department of Mathematics
Indian Institute of Technology, Bombay
Powai, Mumbai 400076 India
E-mail: {srg, jkv}

Version 1.21, November 2000


Basics of the theory of primary decomposition of modules are outlined here. The notions of graded rings and modules are also introduced, and then the special features of primary decomposition in the case of graded modules are discussed. These notes are a slightly revised and expanded version of the second chapter of the Lecture Notes of the NBHM Instructional Conference on Combinatorial Topology and Algebra, held at IIT Bombay in December 1993. As such they may be viewed as a continuation of the Quick Review.


Introduction 2
1 Associated Primes 2
2 Primary Decomposition 5
3 Graded Rings and Modules 7
4 Primary Decomposition in Graded Modules 11
References 13

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