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We define the concept of a doset Hibi ring and a generalized doset Hibi ringwhich are subrings of a Hibi ring and are normal affine semigrouprings. Weapply the theory of (generalized) doset Hibi rings to analyze the rings ofabsolute orthogonal invariants and absolute special orthogonal invariants andshow that these rings are normal and Cohen-Macaulay and has rationalsingularities if the characteristic of the base field is zero and is F-rationalotherwise. We also state criteria of Gorenstein property of these rings.

Doset Hibi rings with an application to invariant theory