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Fundamentalnaya i Prikladnaya Matematika, 2010, Volume 16, Issue 3, Pages 41–62 (Mi fpm1319)  
Global dimension of Noetherian serial rings

N. A. Bronickaya, V. V. Kirichenko

National Taras Shevchenko University of Kyiv
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Abstract: The global dimension of Noetherian serial rings is studied. It is proved that if an indecomposable serial ring has infinite global dimension then it is Artinian and its quiver is a simple cycle. Using methods of the theory of right serial quivers, we give an upper estimate on the Loewy length of Artinian rings of finite global dimension. Applications to the calculation of the global dimension of tiled orders of width 2 are given.
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 177, Issue 6, Pages 801–816
DOI: https://doi.org/10.1007/s10958-011-0510-8
Bibliographic databases:
Document Type: Article
UDC: 512.552.1
Language: Russian
Citation: N. A. Bronickaya, V. V. Kirichenko, “Global dimension of Noetherian serial rings”, Fundam. Prikl. Mat., 16:3 (2010), 41–62; J. Math. Sci., 177:6 (2011), 801–816
Citation in format AMSBIB
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\by N.~A.~Bronickaya, V.~V.~Kirichenko
\paper Global dimension of Noetherian serial rings
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 3
\pages 41--62
\mathnet{http://mi.mathnet.ru/fpm1319}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2786529}
\transl
\jour J. Math. Sci.
\yr 2011
\vol 177
\issue 6
\pages 801--816
\crossref{https://doi.org/10.1007/s10958-011-0510-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052388328}
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