LaTorre, D. R. The Brown-McCoy radicals of a hemiring. (English) Zbl 0189.33102 Publ. Math. Debr. 14, 15-28 (1967). Let \(C\) denote the class of all additively commutative semirings and with each \(S\) in \(C\) associate a fined mapping \(F_S\) of \(C\) into the collection of all non-empty subsets of \(S\) subject to the following condition: If \(S\) and \(\Sigma\) are in \(C\), if \(\Phi\colon a\to \bar a\) is a homomorphism of \(S\) onto \(\Sigma\), and if \(F_S(a)\) is the image, under \(\Phi\), of the subset \(F_(a)\) of \(S\), then \(\overline{F_S(a)}\subseteq F_\Sigma(\bar a)\). An element \(a\) in a semiring \(S\) is called \(F_S\)-regular provided \(a\in F_S(a)\), and a complex \(M\) of \(S\) is said to be an \(F_S\)-regular subset of \(S\) if every element of \(M\) is an \(F_S\)-regular element of \(S\). The \(F\)-radical [\(FK\)-radical, \(FH\)-radical] of a semiring \(S\) is the set of all elements \(b\) in \(S\) for which the principal semi-ideal \((b)\) [\(k\)-ideal \((b)_k\), \(h\)-ideal \((b)_h\)] is an \(F_S\)-regular subset of \(S\). A hemiring \(S\) is said to be of type \((H)\) provided that if \(I\) is an \(h\)-ideal of \(S\), and \(\nu\) is the natural homomorphism of \(S\) onto \(S/I\), then the image, under \(nu\), of any \(h\)-ideal of \(S\) is an \(h\)-ideal of \(S/I\). After restricting the mapping \(F_S\) and imposing an additional condition, the author considers the \(FH\) radical only. He characterizes the \(FH\)-radical of a hemiring of type \((H)\) as the intersection of a class of \(h\)-ideals. Finally he discusses a special case of the \(FH\)-radical, namely the \(H\)-radical of a hemiring of type \((H)\). Reviewer: S. M. Yusuf Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 16Y99 Generalizations 16Y60 Semirings Keywords:Brown-McCoy radicals; hemiring PDFBibTeX XMLCite \textit{D. R. LaTorre}, Publ. Math. Debr. 14, 15--28 (1967; Zbl 0189.33102)