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Hacque-Amitsur rings. (English. Russian original) Zbl 0842.16017

Algebra Logic 34, No. 2, 101-111 (1995); translation from Algebra Logika 34, No. 2, 190-210 (1995).
Summary: We consider a class of rings that combines classes from a theorem of Amitsur and the classes characterized by Hacque. A structure theorem is proved, and we use it to describe left nonsingular Amitsur rings with finite left Goldie dimension.

MSC:

16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
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References:

[1] S. A. Amitsur, ?Rings of quotients and Morita contexts,?J. Alg.,17, 273-298 (1971). · Zbl 0221.16014
[2] M. Hacque, ?Que’lques remarques sur la notion de socle,?Commun. Algebra,10, 1003-1025 (1982). · Zbl 0495.16030
[3] M. Hacque, ?Anneaux fid’element repre’sente’s sur leur socle droit,?Commun. Algebra,10, 1027-1072 (1982). · Zbl 0495.16012
[4] N. Jacobson, ?Structure of Rings,?Coll. Publ. Am. Math. Soc.,37, (1964). · Zbl 0117.03301
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