Serial rings and their generalizations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 3-27
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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.
@article{BASM_2011_1_a0,
author = {Vladimir Kirichenko and Makar Plakhotnyk},
title = {Serial rings and their generalizations},
journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
pages = {3--27},
publisher = {mathdoc},
number = {1},
year = {2011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BASM_2011_1_a0/}
}
TY - JOUR AU - Vladimir Kirichenko AU - Makar Plakhotnyk TI - Serial rings and their generalizations JO - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica PY - 2011 SP - 3 EP - 27 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BASM_2011_1_a0/ LA - en ID - BASM_2011_1_a0 ER -
Vladimir Kirichenko; Makar Plakhotnyk. Serial rings and their generalizations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 3-27. http://geodesic.mathdoc.fr/item/BASM_2011_1_a0/