Let $R=S/I$ be a graded algebra with $t_i$ and $T_i$ being the minimal andmaximal shifts in the minimal $S$ resolution of $R$ at degree $i$. In thispaper we prove that $t_n\leq t_1+T_{n-1}$, for all $n$ and as a consequence, weshow that for Gorenstein algebras of codimension $h$, the subadditivity ofmaximal shifts $T_i$ in the minimal resolution holds for $i \geq h-1$, i.e, weshow that $T_i \leq T_a+T_{i-a}$ for $i\geq h-1$.
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机译：假设$ R = S / I $是一个等级代数，其中$ t_i $和$ T_i $是度数$ i $的最小$ S $分辨率$ R $的最小和最大位移。在本文中，我们证明了$ t_n \ leq t_1 + T_ {n-1} $，对于所有$ n $，因此，我们证明，对于余维$ h $的Gorenstein代数，最大的可加性将$ T_i $最小地移位。分辨率适用于$ i \ geq h-1 $，即，我们显示$ T_i \ leq T_a + T_ {ia} $为$ i \ geq h-1 $。
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