Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2011, Number 1, Pages 3–27 (Mi basm275)  
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Serial rings and their generalizations

Vladimir Kirichenko, Makar Plakhotnyk

Mech-Math. Dept., Kyiv Taras Shevchenko Univ., Kyiv, Ukraine
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Abstract: We give a survey of results on the theory of semiprime semidistributive rings, in particular, serial rings. Besides this we prove that a serial ring is Artinian if and only if some power of its Jacobson radical is zero. Also we prove that a serial ring is Noetherian if and only if the intersection of all powers of Jacobson radical is zero. These two theorems hold for semiperfect semidistributive rings.
Keywords and phrases: serial ring, SPSD-ring, quiver of ring.
Received: 06.12.2010
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Document Type: Article
MSC: 16L30
Language: English
Citation: Vladimir Kirichenko, Makar Plakhotnyk, “Serial rings and their generalizations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2011, no. 1, 3–27
Citation in format AMSBIB
\Bibitem{KirPla11}
\by Vladimir~Kirichenko, Makar~Plakhotnyk
\paper Serial rings and their generalizations
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2011
\issue 1
\pages 3--27
\mathnet{http://mi.mathnet.ru/basm275}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2849224}
\zmath{https://zbmath.org/?q=an:1235.16018}
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