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Lanski, Charles; Resco, Richard; Small, Lance

On the primitivity of prime rings. (English) Zbl 0412.16002

J. Algebra 59, 395-398 (1979).
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Cited in 1 Review
Cited in 22 Documents

MSC:

16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16N60 Prime and semiprime associative rings
16W50 Graded rings and modules (associative rings and algebras)
16U99 Conditions on elements
16Kxx Division rings and semisimple Artin rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)

Keywords:

prime ring; nonzero idempotent; primitive ring; primitive F-algebra with nonzero socle; division algebra; left annihilator
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References:

[1] S. A. Amitsur and L. W. SmallIsrael J. Math.; S. A. Amitsur and L. W. SmallIsrael J. Math. · Zbl 0395.16013
[2] Formanek, E., Group rings of free products are primitive, J. Algebra, 26, 508-511 (1973) · Zbl 0266.16008
[3] Jacobson, N., Structure of Rings, (Amer. Math. Soc. Colloquium Publications, Vol. 37 (1964), Amer. Math. Soc.,: Amer. Math. Soc., Providence, R.I.) · JFM 65.1131.01
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