Survey articles

Serial rings and their generalizations

Vladimir Kirichenko, Makar Plakhotnyk

Mech-Math. Dept., Kyiv Taras Shevchenko Univ., Kyiv, Ukraine

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.

MSC: 16L30

Received: 06.12.2010

Language: English

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