Geodesic
On the product of all nonzero elements of a finite ring
Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 325-330

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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. 
Hermann, Peter Z. On the product of all nonzero elements of a finite ring. Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 325-330. doi: 10.1017/S0017089500007412
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[1] 1.Bondy, J. A. and Murty, U. S. R., Graph theory with applications (Macmillan, 1976). Google Scholar | DOI

[2] 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] 3.Dirac, G. A., Some theorems on abstract graphs, Proc. Lond Math. Soc. (3) 2 (1952), 69–81. Google Scholar | DOI

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