Structure of genera of representations of nonsemisimple rings

  • Yu. A. Drozd
Article

Abstract

The investigation of integral representations of arbitrary rings is shown to be equivalent to the case of orders in semisimple algebras. An example is constructed showing that, for an order in a nonsemisimple algebra, the number of representations in the genus may increase without limit with varying genera.

Keywords

Integral Representation Arbitrary Ring 

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Literature cited

  1. 1.
    D. K. Faddeev, “The semigroup of genera in integral-representation, theory,” Izv. AN SSSR, Ser. Matem.,28, 475–478 (1964).Google Scholar
  2. 2.
    M. Eichler, “Über die Idealklassenzahl hyperkomplexer Systeme,” Math. Z.,43, 481–494 (1938).Google Scholar
  3. 3.
    H. Jacobinski, “Genera and decompositions of lattices over orders,” Acta Math.,121, 1–29 (1968).Google Scholar
  4. 4.
    Yu. A. Drozd, “Abelian and integral representations,” Izv. AN SSSR, Ser. Matem.,33, 1080–1088 (1969).Google Scholar
  5. 5.
    A. V. Roiter, “Integral representations belonging to a single genus,” Izv. AN SSSR, Ser. Matem.,30, 1351–1324 (1966)Google Scholar
  6. 6.
    D. K. Faddeev, “Introduction to the multiplicative theory of modules of integral representations,” Trudy Matematicheskogo In-ta im. V. A. Steklova AN SSSR,80, 145–182 (1965).Google Scholar
  7. 7.
    D. K. Faddeev, “The equivalence of integral-matrix systems,” Izv. AN SSSR, Ser. Matem.,30, 445–454 (1966).Google Scholar

Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1972

Authors and Affiliations

  • Yu. A. Drozd
    • 1
  1. 1.Kiev State UniversityUSSR

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