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Characterization of finite Frobenius rings

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Abstract.

It is shown that a finite ring R is a Frobenius ring if and only if \(_R(R/\hbox {Rad}\, R)\cong \hbox {Soc}\, (_RR)\). Other combinatorial characterizations of finite Frobenius rings are presented which have applications in the theory of linear codes over finite rings.

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  1. Zentrum Mathematik, Technische Universität München, D-80290 München, Germany, , , , , , DE

    T. Honold

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  1. T. Honold
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Received: 20.10.1999

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Honold, T. Characterization of finite Frobenius rings. Arch. Math. 76, 406–415 (2001). https://doi.org/10.1007/PL00000451

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  • DOI: https://doi.org/10.1007/PL00000451

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