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On uniformly strongly prime gamma rings. (English) Zbl 0638.16031

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

MSC:

16Y60 Semirings
16Nxx Radicals and radical properties of associative rings
16S50 Endomorphism rings; matrix rings
16N60 Prime and semiprime associative rings
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References:

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