Booth, G. L.; Groenwald, N. J. On uniformly strongly prime gamma rings. (English) Zbl 0638.16031 Bull. Aust. Math. Soc. 37, No. 3, 437-445 (1988). The authors introduce the concepts of uniformly strong prime (usp) \(\Gamma\)-rings and a usp radical T(M) for a \(\Gamma\)-ring M. If \(M_{mn}\) is the matrix \(\Gamma_{nm}\)-ring, \(T(M_{mn})=(T(M))_{mn}\). It is proved that T is a special radical in the variety of \(\Gamma\)-rings. If \(T_ 1\) is the upper radical determined by the class of usp \(\Gamma\)-rings of bound 1, then \(T\subseteq T_ 1\) but the reverse inclusion is not true in general. Reviewer: S.M.Yusuf Cited in 3 Documents MSC: 16Y60 Semirings 16Nxx Radicals and radical properties of associative rings 16S50 Endomorphism rings; matrix rings 16N60 Prime and semiprime associative rings Keywords:uniformly strong prime \(\Gamma \)-rings; matrix \(\Gamma _{nm}\)-ring; special radical; upper radical PDFBibTeX XMLCite \textit{G. L. Booth} and \textit{N. J. Groenwald}, Bull. Aust. Math. Soc. 37, No. 3, 437--445 (1988; Zbl 0638.16031) Full Text: DOI References: [1] Kyuno, Pacific J. Math. 98 pp 375– (1982) · Zbl 0432.16021 · doi:10.2140/pjm.1982.98.375 [2] Kyuno, Math. Japon 24 pp 191– (1979) [3] Kyuno, Pacific J. Math. 75 pp 185– (1978) · Zbl 0381.16022 · doi:10.2140/pjm.1978.75.185 [4] Booth, Quaestiones Math. 7 pp 251– (1984) · Zbl 0555.16023 · doi:10.1080/16073606.1984.9632335 [5] Coppage, J. Math. Soc. Japan 23 pp 40– (1971) [6] DOI: 10.1016/0021-8693(73)90143-9 · Zbl 0253.16007 · doi:10.1016/0021-8693(73)90143-9 [7] Booth, Math. Japon. 31 pp 175– (1986) [8] Heyman, J. Austral. Math. Soc. Ser A 23 pp 340– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.