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On The Commutativity of J-Rings

Published online by Cambridge University Press:  20 November 2018

Jiang Luh
Jiang Luh*
Affiliation:
Wright State University, Dayton, Ohio
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A ring R is called a J-ring if there exists an integer n > 1 such that xn = x for every x ∈ R. The following beautiful theorem due to Jacobson (4, 5) is a generalization of Wedderburn's theorem, which asserts that every finite division ring must be a field.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1289 - 1292
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Ayoub, R. and Ayoub, C., On the commutativity of rings, Amer. Math. Monthly, 71 (1965), 267–271.Google Scholar
2. Herstein, I. N., Wedderburn's theorem and a theorem of Jacobson, Amer. Math. Monthly, 68 (1961), 249–251.Google Scholar
3. Herstein, I. N., Topics in algebra (New York, 1964).Google Scholar
4. Jacobson, N., Structure theory for algebraic algebras of bounded degree, Ann. of Math., 46 (1945), 695–707.Google Scholar
5. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloquium Publications, No. 37, rev. ed. (Providence, 1964).Google Scholar
6. Luh, J., On the structure of J-rings, Amer. Math. Monthly, 74 (1967), 164–166.Google Scholar