Geodesic
Special (p;q) Radicals
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 38-44

Voir la notice de l'article provenant de la source Cambridge University Press

In [3], the study of (p;q) radicals was initiated. In this paper, the integral polynomials p(x) and q(x) which determine the Jacobson radical are characterized and the Jacobson radical is shown to be the only semiprime (p;q) radical for which all fields are semisimple. Also, it is observed that the prime, nil, and Brown-McCoy radicals are not (p;q) radicals. To show that the semiprime (p;q) radicals are special and that they can be determined by subclasses of the class of primitive rings, a classification theorem for (p;q)-regular primitive rings is given. Finally, it is shown that the collection of semiprime (p;q) radicals and the collection of semiprime (p;1) radicals coincide. 
Jr., J. D. McKnight; Musser, Gary L. Special (p;q) Radicals. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 38-44. doi: 10.4153/CJM-1972-005-2
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[1] 1. Andrunakievič, V., Radicals of associative rings. I, Mat. Sb. 44 (1958), 179–212. Google Scholar

[2] 2. Divinsky, N. J., Rings and radicals (Univ. of Toronto Press, Toronto, 1965). Google Scholar

[3] 3. Musser, G. L., Linear semiprime (p;q) radicals, Pacific J. Math. 37 (1971), 749–757. Google Scholar

[4] 4. Snider, R. L., Lattices of radicals, Pacific J. Math. 39 (1971). Google Scholar

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