Abstract
LetR be ans-unital ring, and we prove a commutativity theorem ofR satisfying the following conditions: (1) For eachx, y εR, there exist bounded positive integersk=k(x,y), s=s(x,y), t=t(x,y) (where, at least one ofk, s, t is not equal to 1) such that (xy)k=x syt, (xy)k+1=x s+1 y t+1; (2)N, the set of all nilpotent elements ofR, isp-torsion free, wherep is the L. C. M. (least common multiple) of allk, s, t.
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References
Yin Zhiyun. On the commutativity for associative rings. Journal Cent South Inst Min Metall (in Chinese), 1985, (4) : 117–123
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Project supported by The Science Foundation of NECC for Returns
Synopsis of the first author Yin Zhiyun, professor, born in May, 1960, study fields are commutative algebras and economical mathematics.
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Yin, Z., Huang, L. A commutativity condition fors-unital rings. J. Cent. South Univ. Technol. 2, 81–83 (1995). https://doi.org/10.1007/BF02652013
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DOI: https://doi.org/10.1007/BF02652013