Doset Hibi rings with an application to invariant theory
نویسنده
چکیده
We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute orthogonal invariants and special orthogonal invariants and show that these rings are normal and CohenMacaulay and has rational singularities if the characteristic of the base field is zero and is F-rational otherwise. We also state a criterion of Gorenstein property of these rings.
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