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Let $M$ be a positive graded finitely generated module over a positive graded commutative ring $R$. Assume that $R_0$ is a local ring with maximal ideal $m_0$. Let $d$ be the Krull dimension of $M$. In the book "Local cohomology : An algebraic introduction with geometric application" of R.Y. Sharp and Broddman, the author claim that if $d=0$ then the set of associated primes ideal of $M$ is $\lbrace m_0 \oplus R_+ \rbrace$, and therefore there exist a $t\in \mathbb{N}$ such that :$R_{+}^{t}M=0$.

My question is :

1. Why Ass(M)= $\lbrace m_0 \oplus R_+ \rbrace$

2. Why from that we have :$R_{+}^{t}M=0$ for some $t\in \mathbb{N}$ ?

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# Question on local cohomology

Let $M$ be a positive graded finitely generated module over a positive graded commutative ring $R$. Assume that $R_0$ is a local ring with maximal ideal $m_0$. Let $d$ be the Krull dimension of $M$. In the book "Local cohomology : An algebraic introduction with geometric application" of R.Y. Sharp and Broddman, the author claim that the set of associated primes ideal of $M$ is $\lbrace m_0 \oplus R_+ \rbrace$, and therefore there exist a $t\in \mathbb{N}$ such that :$R_{+}^{t}M=0$.

My question is :

1. Why Ass(M)= $\lbrace m_0 \oplus R_+ \rbrace$

2. Why from that we have :$R_{+}^{t}M=0$ for some $t\in \mathbb{N}$ ?