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)


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
$$S = \left\{ {a{f^{ - 1}}\left| {a \in {F_n}} \right.,f \in F} \right\}$$


Left Ideal Prime Ring Regular Element Endomorphism Ring Regular Ring 
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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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