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Algebra pp 388-401 | Cite as

Noetherian Semiprime Rings

  • Carl Faith
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 190)

Abstract

A ring S is a (classical) right quotient ring of a subring T if every regular element aT has an inverse in S and
$$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$
Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, bT, and if b is regular, then there exist a 1, b 1T, b 1 regular, such that ab 1 = ba 1 (see 9.1). If T is commutative, this condition is automatic, and if T is a domain, this is the Ore condition.

Keywords

Prime Ring Regular Element Noetherian Ring Matrix Ring Quotient Ring 
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-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

  • Carl Faith
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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