A commutative ring R is said to be nonnil-Noetherian if every ideal which is not contained in the nil-radical of R is finitely generated. We show that many of the properties of Noetherian rings are true for nonnil-Noetherian rings. Then we study the rings of formal power series over a nonnil-Noetherian ring. We prove that if R is an SFT nonnil-Noetherian ring then dim R[[X_1,..., X_n]] = dim R n and that the ring R[[X_1,...,X_n]] is also SFT. We provide an answer to an open question concerning the relationship between the nilradical of R and the nilradical of R[[X]] [6, page 284]. We prove that, for a commutative ring R, Nil (R)[[X_1,... ,X_n]] = Nil (R[[X_1,..., X_n]]) if and only if Nil (R) is an SFT ideal of R, and in that case Nil (R[[X_1,...,X_n]]) is also an SFT ideal of R[[X_1,..., X_n]].
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机译：如果有限地产生不包含在R的基团中的每个理想值，则称可交换环R是非nil-Noetherian。我们证明了Noetherian环的许多特性对于nonnil-Noetherian环都是正确的。然后，我们研究非零-诺瑟环上的形式幂级数环。我们证明如果R是一个SFT非零-Noetherian环，则dim R [[X_1，...，X_n]] = dim R n，并且环R [[X_1，...，X_n]]也是SFT。我们提供了一个有关R的基数与R [[X]]的基数之间的关系的悬而未决的问题的答案[6，第284页]。我们证明，对于交换环R，当且仅当Nil（R）为N时，Nil（R）[[X_1，...，X_n]] = Nil（R [[X_1，...，X_n]]）= R的SFT理想值，在这种情况下Nil（R [[X_1，...，X_n]]）也是R [[X_1，...，X_n]]的SFT理想值。
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