The abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classifiy the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.

MSC Classifications:

11E81, 13H10 show english descriptions Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 11E81 - Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
13H10 - Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

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