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On pi-regular rings whose primitive factor rings are Artinian. (English) Zbl 0457.16006


MSC:

16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16U99 Conditions on elements
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16Kxx Division rings and semisimple Artin rings
16P20 Artinian rings and modules (associative rings and 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] Armendariz, E. P.; Fisher, J. W.; Snider, R. L., On injective and surjective endomorphisms of finitely generated modules, Comm. Algebra, 6, 7, 659-672 (1978) · Zbl 0383.16014
[2] Azumaya, G., Strongly π-regular rings, J. Fac. Sci. Hokkaido Univ., 13, 34-39 (1954) · Zbl 0058.02503
[3] Burgess, W. D.; Stephenson, W., An analogue of the Pierce sheaf for non-commutative rings, Comm. Algebra, 6, 9, 863-886 (1978) · Zbl 0374.16017
[4] W.D. Burgess and W. Stephenson, Mi; W.D. Burgess and W. Stephenson, Mi
[5] Dischinger, F., Sur les anneaux fortement π-réguliers, C.R. Acad. Sci. Paris, 283 A, 571-573 (1976) · Zbl 0338.16001
[6] Goodearl, K. R., Von Neumann regular rings (1979), Pitman: Pitman London, San Francisco, Melbourne · Zbl 0411.16007
[7] Hirano, Y., Some studies on strongly π-regular rings, Math. J. Okayama Univ., 20, 2, 141-149 (1978) · Zbl 0394.16011
[8] Jacobson, N., Structure of rings (1964), Amer. Math. Coll. Pub. 37: Amer. Math. Coll. Pub. 37 Providence, RI
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