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Algebra pp 401-417 | Cite as

Orders in Semilocal Matrix Rings

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

Abstract

A ring R is semilocal if R/rad R is semisimple. [Since R/rad R is semiprime, by the W-A Theorem 8.8, this is equivalent to the requirement that R/rad R is right (or left) Artinian.] The main theorem in this chapter is the determination of right orders in semilocal matrix rings D n. A right order R of a ring S is a subring-1 such that
$$S = \left\{ {a{f^{ - 1}}\left| {a \in {F_n}} \right.,f \in F} \right\}$$

Keywords

Left Ideal Prime Ring Regular Element Endomorphism Ring Regular 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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