Prime and Primitive Rings

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


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.)


Prime Ideal Left Ideal Prime Ring Division Ring Density Theorem 
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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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