Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The prime radical in special Jordan rings


Authors: T. S. Erickson and S. Montgomery
Journal: Trans. Amer. Math. Soc. 156 (1971), 155-164
MSC: Primary 17.40; Secondary 16.00
MathSciNet review: 0274543
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Abstract: If R is an associative ring, we consider the special Jordan ring $ {R^ + }$, and when R has an involution, the special Jordan ring S of symmetric elements. We first show that the prime radical of R equals the prime radical of $ {R^ + }$, and that the prime radical of R intersected with S is the prime radical of S. Next we give an elementary characterization, in terms of the associative structure of R, of primeness of S. Finally, we show that a prime ideal of R intersected with S is a prime Jordan ideal of S.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0274543-4
Keywords: Special Jordan ring, prime ring, prime ideals, prime radical, lower nil radical
Article copyright: © Copyright 1971 American Mathematical Society