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On the product of all nonzero elements of a finite ring

Published online by Cambridge University Press:  18 May 2009

Peter Z. Hermann
Peter Z. Hermann
Affiliation:
Department of Algebra and Number Theory, Eötvös Lorànd University, H-1088 Budapest, Mùzeum Krt. 6–8, Hungary
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The aim of the present note is to describe the possible products when taking all the nonzero elements of a finite ring in some sequence. Compared with the analogous situation for finite groups, where the set of products of all elements has been shown in [2] to be a whole coset of the derived group, for rings the set of the above mentioned products will be proved either to be as large as possible or to consist of one or two elements only.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 325 - 330
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Bondy, J. A. and Murty, U. S. R., Graph theory with applications (Macmillan, 1976).CrossRefGoogle Scholar
2.Dénes, J. and Hermann, P. Z., On the product of all elements in a finite group, Ann. Discrete Math. 15 (1982), 105–109.Google Scholar
3.Dirac, G. A., Some theorems on abstract graphs, Proc. Lond Math. Soc. (3) 2 (1952), 69–81.CrossRefGoogle Scholar