Vol. 37, No. 3, 1971

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Linear semiprime (p; q) radicals

Gary L. Musser

Vol. 37 (1971), No. 3, 749–757

This paper introduces McKnight’s (p;q)-regularity and (p;q) radicals, a collection of radicals which contains the Jacobson radical and the radicals of regularity and strong regularity among its members. The linear semiprime (p;q) radicals are classified canonically and, as a result of this classification, these radicals can be distinguished by the fields GF(p) and are shown to form a lattice. The semiprime (p;q) radicals are found to be hereditary and the linear semiprime (p;q) radical of a complete matrix ring of a ring R is determined to be the complete matrix ring over the (p;q) radical of R. More generally, the (p;q) radical of a complete matrix ring over R is contained in the matrix ring over the (p;q) radical of R for all (p;q) radicals.

Mathematical Subject Classification
Primary: 16A21
Received: 6 November 1969
Revised: 23 October 1970
Published: 1 June 1971
Gary L. Musser