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dg near rings on the infinite dihedral group

Published online by Cambridge University Press:  14 February 2012

J. J. Malone
J. J. Malone
Affiliation:
Worcester Polytechnic Institute, Worcester, Mass., USA
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Synopsis

It is shown that exactly six non-isomorphic distributively generated near rings can be defined on the infinite dihedral group. One has the null multiplication, two have trivial multiplications in which the group of left annihilators has index two, and three are distributive and have their product sets equal to a subgroup of order 2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 67 - 70
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Lyons, C. G. and Malone, J. J.Finite dihedral groups and d.g. near rings II. Compositio Math. 26 (1973), 249–259.Google Scholar
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4Meldrum, J. D. P.The endomorphism near-ring of an infinite dihedral group. Proc. Roy. Soc. Edinburgh Sect. A. 76 (1977), 311–321.CrossRefGoogle Scholar
5Willhite, M. L.Distributively generated near rings on the dihedral group of order eight (College Station: Texas A & M Univ. Thesis, 1970).Google Scholar