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Guseva, I. L.

On tensor products of semiprime algebras which are Goldie rings. (English) Zbl 0233.16006

Algebra Logic 9(1970), 378-389 (1972).
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MSC:

16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16N60 Prime and semiprime associative rings
16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
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References:

[1] N. Jacobson, Theory of Rings [Russian translation], IL, Moscow (1947). · Zbl 0029.10601
[2] A. W. Goldie, ”Semi-prime rings with maximum condition,” Proc. London Math. Soc., Ser. 3, 10, No. 38, 201–220 (1960). · Zbl 0091.03304 · doi:10.1112/plms/s3-10.1.201
[3] A. S. Amitsur, ”Rational identities and applications to algebra and geometry,” J. Algebra,3, No. 3, 304–359 (1966). · Zbl 0203.04003 · doi:10.1016/0021-8693(66)90004-4
[4] N. Jacobson, Structure of Rings [Russian translation], IL, Moscow (1961). · Zbl 0098.25901
[5] A. I. Mal’tsev, ”On the representation of infinite algebras,” Matem. Sbornik,13, Nos. 2, 3 (1943).
[6] B. L. van der Waerden, Modern Algebra, Vol. 1 [Russian translation], Gostekhizdat (1947).
[7] E. C. Posner, ”Prime rings satisfying a polynomial identity,” Proc. Amer. Math. Soc.,11, No. 2, 180–183 (1960). · Zbl 0215.38101 · doi:10.1090/S0002-9939-1960-0111765-5
[8] A. V. Jategoankar, ”Ore domains and free algebras,” Bull. London Math. Soc.,1, 45–46 (1969). · Zbl 0175.03001 · doi:10.1112/blms/1.1.45
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