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Fundam. Prikl. Mat., 1995, Volume 1, Issue 2, Pages 565–568 (Mi fpm82)  

This article is cited in 8 scientific papers (total in 8 papers)

Short communications

Von Neumann regular skew-Laurent series rings

K. Sonin

M. V. Lomonosov Moscow State University

Abstract: Let $\varphi$ be an automorphism of finite order. Then the skew-Laurent series ring $A((x,\varphi))$ is von Neumann regular iff $A$ is semisimple Artinian. The third equivalent condition is that $A((x,\varphi))$ is semisimple Artinian. The same result for strong regularity is proved in the case of an arbitrary automorphism $\varphi$.

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Bibliographic databases:
UDC: 512.55
Received: 01.04.1995

Citation: K. Sonin, “Von Neumann regular skew-Laurent series rings”, Fundam. Prikl. Mat., 1:2 (1995), 565–568

Citation in format AMSBIB
\Bibitem{Son95}
\by K.~Sonin
\paper Von Neumann regular skew-Laurent series rings
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 2
\pages 565--568
\mathnet{http://mi.mathnet.ru/fpm82}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1790989}
\zmath{https://zbmath.org/?q=an:0867.16024}


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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. K. Sonin, “Semiprime and semiperfect rings of Laurent series”, Math. Notes, 60:2 (1996), 222–226  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Sonin, KI, “Biregular Lourent series rings”, Vestnik Moskovskogo Universiteta Seriya 1 Matematika Mekhanika, 1997, no. 4, 20  mathscinet  zmath  isi
    3. Tuganbaev D.A., “Some ring and module properties of skew Laurent series”, Formal Power Series and Algebraic Combinatorics, 2000, 613–622  crossref  mathscinet  zmath  isi
    4. A. A. Tuganbaev, “The Jacobson radical of the Laurent series ring”, J. Math. Sci., 149:2 (2008), 1182–1186  mathnet  crossref  mathscinet  zmath
    5. D. A. Tuganbaev, “Laurent rings”, J. Math. Sci., 149:3 (2008), 1286–1337  mathnet  crossref  mathscinet  zmath
    6. D. A. Tuganbaev, “Malcev rings”, Discrete Math. Appl., 18:2 (2008), 207–225  mathnet  crossref  crossref  mathscinet  zmath  elib
    7. Mazurek, R, “On von Neumann regular rings of skew generalized power series”, Communications in Algebra, 36:5 (2008), 1855  crossref  mathscinet  zmath  isi
    8. Moussavi A., “on Radicals of Skew Inverse Laurent Series Rings”, Algebr. Colloq., 23:2 (2016), 335–346  crossref  isi
  • Фундаментальная и прикладная математика
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