**Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 533-549 (1999)
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On the Radical Theory for Semirings

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Bettina Morak

Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, 09596 Freiberg, Germany

**Abstract:** Based on an abstract concept of radical classes for semirings introduced by D. M. Olson and T. L. Jenkins in [OJ] we develop in this paper a Kurosh-Amitsur radical theory for semrings in a self-contained way. We define radical operators and semisimple classes for semirings independently on radical classes and exhibit among other results the bijective correspondence between each pair of these three concepts. As a special result we obtain that each radical class of semirings satisfies the A-D-S-property, which yields that each semisimple class is hereditary. We give more details in the introduction, where we also compare Kurosh-Amitsur radical theories for different structures. Observing the remarks given there, a reader may well use this paper also to inform himself about the radical theory for associative rings. \item{[OJ]} Olson, D. M.; Jenkins, T. L.: * Radical theory for hemirings.* J. Natur. Sci. Math. ** 23** (1983), 23-32.

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