This article is cited in 5 papers

Characterization of one radical of group rings over finite prime fields

A. I. Kornev, T. V. Pavlova

Omsk State Pedagogical University

Abstract: We study complete and reduced associative rings (in the sense of L. M. Martynov). We prove a necessary and sufficient test for completeness of a semigroup ring, calculate the greatest complete subring (which is an ideal) of a group ring over finite prime fields, and characterize the reduced group rings of finite groups over finite prime fields.

Keywords: group ring, semigroup ring, complete ring, Kurosh–Amitsur radical.

UDC: 512.552.7

Received: 14.11.2003

 English version: Siberian Mathematical Journal, 2004, 45:3, 504–512

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