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- W1972504509 abstract "A new ring transpormation T ( bA ) (for each non-nilpotent b in a Noetherian ring A ) is introduced and it is shown that T ( bA ) is always a finite A -module and is the largest transformation of its type that has this property. Then, using this transformation on the element u in the Rees ringR( A, I ) of A with respect to an ideal I in A , it is shown that the I-adic topology on A is linearly equivalent to the u -symbolic topology on A ; that is, there exists k ⩾0 such that I n ⊆I [n] ⊆ n − k for all n ≥ k , where I [ n ] = u n T ( u R( A,I ))∩ A . Several corollaries of this are proved, and Cohen-Macaulay rings are characterized in terms of the filtrations I { [ n ] ; n ≥0}, where I is an ideal of the principal class in A ." @default.
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- W1972504509 date "1986-01-01" @default.
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- W1972504509 title "On linearity equivalent ideal topologies" @default.
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- W1972504509 doi "https://doi.org/10.1016/0022-4049(86)90101-5" @default.
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