Some commutativity results for rings with two-variable constraints
HTML articles powered by AMS MathViewer
- by H. E. Bell PDF
- Proc. Amer. Math. Soc. 53 (1975), 280-284 Request permission
Abstract:
It is proved that an associative ring $R$ has nil commutator ideal if for each $x,\;y\epsilon R$, there is a polynomial $p(X)\epsilon X{\mathbf {Z}}[X]$ for which $xy - yp(x)$ is central. Two restrictions on the $p(X)$ which guarantee commutativity are established.References
- Howard E. Bell, Duo rings: Some applications to commutativity theorems, Canad. Math. Bull. 11 (1968), 375–380. MR 234985, DOI 10.4153/CMB-1968-042-0
- Howard E. Bell, On some commutativity theorems of Herstein, Arch. Math. (Basel) 24 (1973), 34–38. MR 320090, DOI 10.1007/BF01228168
- M. Chacron, On a theorem of Herstein, Canadian J. Math. 21 (1969), 1348–1353. MR 262295, DOI 10.4153/CJM-1969-148-5
- I. N. Herstein, A theorem on rings, Canad. J. Math. 5 (1953), 238–241. MR 53082, DOI 10.4153/cjm-1953-025-6
- I. N. Herstein, The structure of a certain class of rings, Amer. J. Math. 75 (1953), 864–871. MR 58580, DOI 10.2307/2372554
- Mohan S. Putcha and Adil Yaqub, Rings satisfying polynomial constraints, J. Math. Soc. Japan 25 (1973), 115–124. MR 313312, DOI 10.2969/jmsj/02510115
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 280-284
- MSC: Primary 16A70
- DOI: https://doi.org/10.1090/S0002-9939-1975-0382357-9
- MathSciNet review: 0382357