Some Recent Developments in Group Near-Rings

John D. P. Meldrum ()
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John D. P. Meldrum: University of Edinburgh

A chapter in Nearrings and Nearfields, 2005, pp 35-55 from Springer

Abstract: Abstract Since their definition in 1984 and subsequent publication in Meldrum and van der Walt [86], matrix near-rings have proved to be a useful and fruitful generalization of matrix rings. The same basic idea was used to define group near-rings, culminating in le Riche, Meldrum and van der Walt [89]. Not surprisingly this construction has not attracted as much attention and effort as matrix near-rings: after all matrix rings are much more commonly used than group rings. There are however some interesting results that have been developed and there are intriguing parallels between matrix near-rings and group near-rings. We present here an account of some of the recent work on group near-rings, emphasizing the parallels with matrix near-rings and the most recent developments. Much of this work was done in collaboration with J. H. Meyer.

Keywords: Group Ring; Wreath Product; Matrix Ring; Augmentation Ideal; Distributor Series (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-3391-9_3

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DOI: 10.1007/1-4020-3391-5_3

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