Certain properties of normal semigroups. (Q5929665)

By a `normal semigroup' the authors mean a semigroup \(S\) in which \(aS=Sa\) for all \(a\in S\). These semigroups were called `duo semigroups' in earlier papers, beginning with \textit{E.~H.~Feller} [Trans. Am. Math. Soc. 89, 79-91 (1958; Zbl 0095.25703)]. In the present paper the authors extend several results of \textit{M.~Satyanarayana} [Czech. Math. J. 21(96), 633-637 (1971; Zbl 0228.20045), ibid. 22(97), 509-516 (1972; Zbl 0248.20072)] from commutative to normal semigroups: they characterize normal semigroups in which every ideal is prime, and prove several properties of such semigroups.