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Algebra Logika, 2013, Volume 52, Number 2, Pages 145–154 (Mi al579)  

This article is cited in 1 scientific paper (total in 1 paper)

An application of the method of orthogonal completeness in graded ring theory

A. L. Kanunnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics. Moscow, Russia

Abstract: A method of orthogonal completeness was devised by K. I. Beidar and A. V. Mikhalev in the 1970s. Initially, the method was applied in ring theory and was mainly used to derive theorems for semiprime rings by reducing the semiprime case to the prime. In the 1980s, the same authors developed a theory of orthogonal completeness for arbitrary algebraic systems. The theory of orthogonal completeness is applied to group-graded rings. To use the Beidar–Mikhalev theorems on orthogonal completeness, a graded ring is treated as an algebraic system with a ring signature augmented by the operation of taking homogeneous components and by homogeneity predicates. The graded analog of Herstein's theorem for prime rings with derivations, as well as its generalization to semiprime rings based on the method of orthogonal completeness, is proved. It is shown that every homogeneous derivation of a graded ring extends to a homogeneous derivation of its complete graded right ring of quotients.

Keywords: graded rings of quotients, orthogonal completeness, rings with derivation.

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English version:
Algebra and Logic, 2013, 52:2, 98–104

Bibliographic databases:

UDC: 512.552
Received: 15.11.2012
Revised: 12.03.2013

Citation: A. L. Kanunnikov, “An application of the method of orthogonal completeness in graded ring theory”, Algebra Logika, 52:2 (2013), 145–154; Algebra and Logic, 52:2 (2013), 98–104

Citation in format AMSBIB
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\pages 145--154
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Kanunnikov, “Graded quotient rings”, J. Math. Sci., 233:1 (2018), 50–94  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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