Modules and Ideals

  • Nathan Jacobson
Part of the Graduate Texts in Mathematics book series (GTM, volume 30)


The concept of a module that we consider in this chapter is a composite notion based on the concepts of a ring and of a group with operators. Modules are of fundamental importance in the study of homomorphisms of abstract rings into rings of endomorphisms of commutative groups (so-called representation theory). This was first recognized by Emmy Noether. Previously the concept of a module had made its appearance in the theory of algebraic numbers.


Primary Ideal Commutative Ring Uniqueness Theorem Left Ideal Noetherian Ring 


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Copyright information

© Nathan Jacobson 1951

Authors and Affiliations

  • Nathan Jacobson
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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