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Archiv der Mathematik

, Volume 78, Issue 5, pp 350–357 | Cite as

Simple artinian rings as sums of nilpotent subrings

  • A. Salwa
  • 42 Downloads

Abstract.

Decompositions of simple artinian rings as additive sums of nilpotent subrings are considered. In particular, necessary and sufficent conditions for minimal decompositions are found in terms of the underlying division ring. This is used to prove that any algebra with 1 can be unitarily embedded into a simple algebra with 1 which is a sum of four subalgebras with zero multiplication and also into a simple algebra which is a sum of three nilpotent subalgebras of degree 3. Since our proof is constructive and is based on simple artinian rings, the latter result can be viewed as an extension and a strengthened version of Bokut's theorem, [2].

Keywords

Simple Algebra Division Ring Zero Multiplication Artinian Ring Strengthened Version 
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

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • A. Salwa
    • 1
  1. 1.Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland,¶ e-mail: asalwa@mimuw.edu.plPL

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