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- W2017360651 abstract "It is well known that if R is a Noetherian ring and b 1 ,…, b h are an R -sequence, then there exist ideals (0) = ( B 0 ⊂ B 1 ⊂… ⊂ B h in R such that the following hold for i = 1,…, h : (a) B i = ( b 1 … b i ) R ; (b) Ass ( R B i ) = ∪ { Ass ( R (B i ) k ) ; k ⩾ 1} (c) ( B i −1) k : b i R = ( B i −1 ) K for all k ⩾ 1; and (d) if p ϵ Ass ( R B i−1 ) and ( p , b i ) R ≠ R , then P is properly contained in some P ϵ Ass ( R B i ) . The main theorem in this paper shows that something quite similar to this holds for essential sequences; namely, if b i ,…, b h are an essential sequence in R , then there exists ideals (0) = J 0 ⊂ J 1 ⊂…⊂ J h in R such that the following hold for i = 1,…, h : (á) J i , is projectively equivalent to ( b i ,…, b i R ; (b′) Ass ( R J i ) = ∪ { Ass ( R (J i ) k ); k ⩾ 1} ; (c′) ( J i −1 ) k : b i R = ( J i −1 ) k for all k ⩾ 1; and (d′) if P ϵ Ass ( R J i−1 and ( p , b i ) R ≠ R , then P is properly contained in some P ϵ Ass ( R J i ) ." @default.
- W2017360651 created "2016-06-24" @default.
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- W2017360651 date "1987-09-01" @default.
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- W2017360651 title "Essential sequences and projective equivalence" @default.
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- W2017360651 doi "https://doi.org/10.1016/0021-8693(87)90145-1" @default.
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