Abstract
The following theorem is proved: ifA andB are twoPI-algebras over a fieldF, thenA⊗ F B is aPI-algebra.
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References
N. Jacobson.,Structure of Rings, Amer. Math. Soc. Colloquim, Publication 37, 2nd edition chapter 10, 1964.
C. Procesi and L. Small,Endomorphism rings of modules over PI-algebra, Math. Z.106 (1968), 178–180.
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This paper was written while the author was doing his Ph.D. thesis at the Hebrew University of Jerusalem under the supervision of Professor A. S. Amitsur, to whom the author wishes to express his warm thanks.
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Regev, A. Existence of identities inA⊗B . Israel J. Math. 11, 131–152 (1972). https://doi.org/10.1007/BF02762615
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DOI: https://doi.org/10.1007/BF02762615