Study of three-dimensional algebras with straightening laws which are Gorenstein domains. III (Q1109836)

Let k be a field, A a polynomial ring in a finite number of indeterminates over k and H a poset with an injection \(\rho:\quad H\to A\) such that \(\rho\) (H) is a set of monomials of A. Then (H,\(\rho)\) is called a toroidal poset, provided \(R_{\rho}=k[\rho (H)]\) is a homogeneous algebra with straightening laws. (H,\(\rho)\) is called Gorenstein, if \(R_{\rho}\) is a Gorenstein ring. Continuing part I and II of this paper [see the author's joint work with \textit{K. Watanabe}, Hiroshima Math. J. 15, 27-54, 321-340 (1985; Zbl 0633.13003 and 13004)] the author gives a classification of Gorenstein toroidal posets (H,\(\rho)\) with \(\dim (R_{\rho})=3\) up to equivalence (see loc. cit.). This is done by the help of certain combinatorial information about posets from a ring theoretical property of an affine semigroup ring given by the author in Nagoya Math. J. 112, 1-24 (1988; Zbl 0627.13001).