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Let $k$ be a field. The homogeneous coordinate ring $k[\\Gamma]$ of the affine monomial curve parametrically defined by $X_0=t^{m_0},X_{1}=t^{m_1},X_2=t^{m_3},Y=t^{n}$ is a graded $R$-module, where $R$ is the polynomial ring $k[X_0,X_1,X_3, Y]$ with the grading $\\deg{X_i}:=m_i, \\deg{Y}:=n$. 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Let $k$ be a field. The homogeneous coordinate ring $k[\\Gamma]$ of the affine monomial curve parametrically defined by $X_0=t^{m_0},X_{1}=t^{m_1},X_2=t^{m_3},Y=t^{n}$ is a graded $R$-module, where $R$ is the polynomial ring $k[X_0,X_1,X_3, Y]$ with the grading $\\deg{X_i}:=m_i, \\deg{Y}:=n$. 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