Rings satisfying monomial identities
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- by Mohan S. Putcha and Adil Yaqub PDF
- Proc. Amer. Math. Soc. 32 (1972), 52-56 Request permission
Abstract:
The following theorem is proved: Suppose R is an associative ring and suppose that $w({x_1}, \cdots ,{x_n})$ is a fixed word distinct from ${x_1} \cdots {x_n}$. If, further, ${x_1} \cdots {x_n} = w({x_1}, \cdots ,{x_n})$, for all ${x_1}, \cdots ,{x_n}$ in R, then the commutator ideal of R is nilpotent. Moreover, it is shown that this theorem need not be true if the word w is not fixed.References
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I. N. Herstein, Theory of rings, Math. Lecture Notes, University of Chicago, Chicago, Ill., 1961.
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- Neal H. McCoy, The theory of rings, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0188241
- Mohan S. Putcha and Adil Yaqub, Semigroups satisfying permutation identities, Semigroup Forum 3 (1971/72), no. 1, 68–73. MR 292969, DOI 10.1007/BF02572944
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 52-56
- MSC: Primary 16.49
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289569-0
- MathSciNet review: 0289569