Semisimple classes and upper-type radical classes of narings
Authors:
Terry L. Jenkins and Daryl Kreiling
Journal:
Proc. Amer. Math. Soc. 26 (1970), 378-382
MSC:
Primary 17.10
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265420-8
MathSciNet review:
0265420
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Abstract | References | Similar Articles | Additional Information
Abstract: In the universal class of associative rings every class $M$ of rings determines a unique upper radical class. It is shown that the same result is valid in the universal class of alternative rings but is not necessarily true in the universal class of narings. The latter class does however determine a type of upper radical.
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- A. G. Kuroš, Radicals of rings and algebras, Mat. Sbornik N.S. 33(75) (1953), 13–26 (Russian). MR 0057236
- W. G. Leavitt and E. P. Armendariz, Nonhereditary semisimple classes, Proc. Amer. Math. Soc. 18 (1967), 1114–1117. MR 220786, DOI https://doi.org/10.1090/S0002-9939-1967-0220786-X
- Yu-lee Lee, On the construction of upper radical properties, Proc. Amer. Math. Soc. 19 (1968), 1165–1166. MR 231850, DOI https://doi.org/10.1090/S0002-9939-1968-0231850-4
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Additional Information
Keywords:
Alternative rings,
upper radical class,
semisimple rings,
upper-type radical classes,
narings
Article copyright:
© Copyright 1970
American Mathematical Society