- 期刊
COMMUTATIVITY THEOREMS FOR RINGS AND GROUPS WITH CONSTRAINTS ON COMMUTATORS
並列摘要
Let n ＞ 1, m, t, s be any positlve integers, and let R be an associative ring with ide:ntity. Suppose x^t[x^n,y] = [x,y^m]l for all x, y in R. If, further, R is n-torsion free, then R is commutativite. If n-torsion freeness of R is replaced by ＂m, n are relatively prime,＂ then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t=s=0 and m=n+1.
延伸閱讀
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- KLEIN, A. A., & BELL, H. E. (2004). A COMMUTATIVITY-OR-FINITENESS CONDITION FOR RINGS. International Journal of Mathematics and Mathematical Sciences, 2004(), 2863-2865-220. https://doi.org/10.1155/S0161171204405420
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- Mamouni, A., Oukhtite, L., & Samman, M. (2012). Commutativity Theorems for ∗-Prime Rings with Differential Identities on Jordan Ideals. ISRN Algebra, (), 158-168. https://doi.org/10.5402/2012/729356