A commutativity theorem for rings
Author:
M. Chacron
Journal:
Proc. Amer. Math. Soc. 59 (1976), 211216
MSC:
Primary 16A70
MathSciNet review:
0414636
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Abstract: Let be any associative ring. Suppose that for every pair there exists a pair such that the elements commute, where the 's are polynomials over the integers with one (central) indeterminate. It is shown here that the nilpotent elements of form a commutative ideal , and that the factor ring is commutative. This result is obtained by the use of the concept of cohypercenter of a ring , which concept parallels the hypercenter of a ring.
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M.
Chacron, On a theorem of Herstein, Canad. J. Math.
21 (1969), 1348–1353. MR 0262295
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N. Herstein, On the hypercenter of a ring, J. Algebra
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N. Herstein, A commutativity theorem, J. Algebra
38 (1976), no. 1, 112–118. MR 0396687
(53 #549)
 [1]
 M. Chacron and G. Thierrin, An algebraic dependence over the quasicentre, Ann. Math. Pura Appl. (to appear). MR 0422351 (54:10341)
 [2]
 M. Chacron, On a theorem of Herstein, Canad. J. Math. 21 (1969), 13481353. MR 41 #6905. MR 0262295 (41:6905)
 [3]
 I. N. Herstein, The structure of a certain class of rings, Amer. J. Math. 75 (1953), 864871. MR 15, 392. MR 0058580 (15:392a)
 [4]
 , On the hypercenter of a ring, J. Algebra (to appear). MR 0371962 (51:8179)
 [5]
 , A commutativity theorem, J. Algebra 38 (1976), 112118. MR 0396687 (53:549)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197604146361
PII:
S 00029939(1976)04146361
Keywords:
Commutator,
polynomials,
quasiregular elements,
subgroups preserved re quasiinner automorphisms
Article copyright:
© Copyright 1976
American Mathematical Society
