Some radical properties of $s$-rings
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- by Michael Rich
- Proc. Amer. Math. Soc. 30 (1971), 40-42
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283034-1
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Abstract:
The class of s-rings includes as a proper subset the classes of associative, alternative, Lie, Jordan, and standard rings. It is shown that in any s-ring R the prime radical of R coincides with the Baer lower radical of R. Relationships between the prime radical and certain other radicals are also given.References
- Bailey Brown and Neal H. McCoy, Prime ideals in nonassociative rings, Trans. Amer. Math. Soc. 89 (1958), 245–255. MR 96713, DOI 10.1090/S0002-9947-1958-0096713-4
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- R. D. Schafer, Standard algebras, Pacific J. Math. 29 (1969), 203–223. MR 244332, DOI 10.2140/pjm.1969.29.203
- Malcolm F. Smiley, Application of a radical of Brown and McCoy to non-associative rings, Amer. J. Math. 72 (1950), 93–100. MR 32591, DOI 10.2307/2372136
- Chester Tsai, The prime radical in a Jordan ring, Proc. Amer. Math. Soc. 19 (1968), 1171–1175. MR 230776, DOI 10.1090/S0002-9939-1968-0230776-X P. J. Zwier, Prime ideals and the prime radical in a class of narings, Notices Amer. Math. Soc. 16 (1969), 660. Abstract #69T-A89.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 40-42
- MSC: Primary 17.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283034-1
- MathSciNet review: 0283034