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Algebra i 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
Full-text PDF (156 kB) Citations (1)
References:
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.
Received: 15.11.2012
Revised: 12.03.2013
English version:
Algebra and Logic, 2013, Volume 52, Issue 2, Pages 98–104
DOI: https://doi.org/10.1007/s10469-013-9225-x
Bibliographic databases:
Document Type: Article
UDC: 512.552
Language: Russian
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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\by A.~L.~Kanunnikov
\paper An application of the method of orthogonal completeness in graded ring theory
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\vol 52
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\pages 145--154
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\pages 98--104
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  • https://www.mathnet.ru/eng/al/v52/i2/p145
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:370
    Full-text PDF :73
    References:68
    First page:22
     
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