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On the radicals of semigroup rings

G. B. Lungu

M. V. Lomonosov Moscow State University

Abstract: The author investigates properties of the radicals of semigroup rings, that can be considered as rings, graded by a band. A characterization of the Brown–McCoy radical of a band-graded ring is obtained. For a semigroup ring of a semilattice it is proved that $\rho(R[\Omega])\subseteq\rho(R)[\Omega]$ holds for any radical $\rho$ (in the sense of Kurosh–Amitsur). The technique of this paper is developed from the one used by W. D. Munn in [3].

UDC: 512.552.12+512.552.7

Received: 01.12.1995

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