Let D be an integral domain. G. Picozza associated to a stable semistar operation \(\star \) on D, a semistar operation \(\star _1\) on the polynomial ring D[X]. We defined the notion of semistar accr domain. We prove that D is \({\widetilde{\star }}\)-Noetherian if and only D[X] is \(\star _1\)-accr. On the other hand, we prove that D satisfies the ascending chain condition on radical quasi-\({\widetilde{\star }}\)-ideals if and only if D[X] satisfies the ascending chain condition on radical quasi-\(\star _1\)-ideals if and only if the Nagata ring of D with respect to the semistar operation \({\widetilde{\star }}\) satisfies the ascending chain condition on radical ideals.

令D为整数域。G. Picozza与D上的稳定半星运算\（\ star \），多项式环D [ X ]上的半星运算\（\ star _1 \）相关联。我们定义了半星accr域的概念。我们证明D是\（{\ widetilde {\ star}} \）- Noetherian，如果并且只有D [ X ]是\（\ star _1 \）- accr。另一方面，我们证明D满足且仅当D [ X时，D满足根基上的\（{\ widetilde {\ star}} \）理想的升链条件。]满足且仅当D的Nagata环相对于半星运算\（{\ widetilde {\ star}} \）满足升序链时，满足拟根\-（\ star _1 \）-理想上的升链条件根本理想的条件。