Rings satisfying monomial constraints

Authors:
Mohan S. Putcha and Adil Yaqub

Journal:
Proc. Amer. Math. Soc. **39** (1973), 10-18

MSC:
Primary 16A38

DOI:
https://doi.org/10.1090/S0002-9939-1973-0313306-5

MathSciNet review:
0313306

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Abstract: The following theorem is proved: Suppose is an associative ring and suppose is the Jacobson radical of . Suppose that for all in , there exists a word , depending on , in which at least one ( varies) is missing, and such that . Then is a nil ring of bounded index and is finite. It is further proved that a commutative nil semigroup satisfies the above identity if and only if it is nilpotent.

**[1]**I. N. Herstein,*Theory of rings*, Lecture Notes, University of Chicago, Chicago, Ill., 1961.**[2]**Nathan Jacobson,*Structure of rings*, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964. MR**0222106****[3]**Irving Kaplansky,*Infinite abelian groups*, University of Michigan Press, Ann Arbor, 1954. MR**0065561****[4]**Trygve Nagell,*Introduction to number theory*, Second edition, Chelsea Publishing Co., New York, 1964. MR**0174513****[5]**Hans Rademacher,*Lectures on elementary number theory*, A Blaisdell Book in the Pure and Applied Sciences, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR**0170844****[6]**B. L. van der Waerden,*Elementarer Beweis eines zahlentheoretischen Existenztheorems*, J. Reine Angew. Math.**171**(1934), 1-3.

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0313306-5

Article copyright:
© Copyright 1973
American Mathematical Society