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Some Recent Developments in Group Near-Rings

In: Nearrings and Nearfields

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  • John D. P. Meldrum

    (University of Edinburgh)

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.

Suggested Citation

  • John D. P. Meldrum, 2005. "Some Recent Developments in Group Near-Rings," Springer Books, in: Hubert Kiechle & Alexander Kreuzer & Momme Johs Thomsen (ed.), Nearrings and Nearfields, pages 35-55, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-3391-9_3
    DOI: 10.1007/1-4020-3391-5_3
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