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π-整环上形式幂级数的容度准则

Keywords: Krull整环,π-整环,形式幂级数,容度

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Abstract:

利用星型算子理论的相关方法,对Krull整环与π-整环进行了研究,给出了π-整环上形式幂级数的一些容度准则,证明了整环R是π-整环当且仅当对f,g∈R[[X]]*,都h∈K[X]*,使得c(f)w=c(g)wc(h)w;当且仅当对f,g∈R[[X]]*,都h∈K[X]*,使得c(f)t=c(g)tc(h)t;当且仅当对f∈R[X]*,g∈R[[X]]*,都h∈K[X]*,使得c(f)w=c(g)wc(h)w;当且仅当对f∈R[X]*,g∈R[[X]]*,都h∈K[X]*,使得c(f)t=c(g)tc(h)t.

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