Rings satisfying Wilson's equality

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1976 English Publisher:Springer Science and Business Media LLCJournal:Periodica Mathematica Hungarica, volume 7, pages 229-232 (issn: 0031-5303, eissn: 1588-2829,

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Authors: Abian, Alexander; Floyd, Denis R.;

doi: 10.1007/bf02017940

Rings satisfying Wilson's equality

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Abstract

A generalization ofWilson's theorem [1] states that the product of all the nonzero elements of a finite field is equal to −1. It is shown here, without assuming the associativity or commutativity of a finite ringR, if the product in any association and permutation of all the nonzero elements ofR is equal to −1 thenR is a field.

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Iowa State University
United States

Keywords

General nonassociative rings, Finite fields and commutative rings (number-theoretic aspects), Finite rings and finite-dimensional associative algebras, Other nonassociative rings and algebras

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