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Prime and Primitive Rings

  • T. Y. Lam
Part of the Problem Books in Mathematics book series (PBM)

Abstract

The notion of prime ideals in commutative rings extends naturally to non-commutative rings. One takes the “same” definition, but replaces the use of elements by ideals of the ring. The Zorn’s Lemma construction of prime ideals disjoint from a multiplicative set in the commutative setting finds a natural generalization, if we just replace the multiplicative set with an “m-system”: cf. FC-(10.5). (A nonempty set SR is called an m-system if, for any a, bS, arbS for some rR.)

Keywords

Prime Ideal Left Ideal Prime Ring Division Ring Density Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • T. Y. Lam
    • 1
  1. 1.Department of Mathematics MA-01University of CaliforniaBerkeleyUSA

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