On ideals whose adic and symbolic topologies are linearly equivalent |
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Institution: | Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. |
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Abstract: | Ideals whose adic and symbolic topologies are linearly equivalent are characterized in terms of analytic spread and u-essential prime divisors. Using this characterization, under certain conditions on a Noetherian ring R and an ideal I of R it is shown that the I-adic and the I-symbolic topologies are linearly equivalent iff gr(I,R)red is a domain, and locally unmixed rings are characterized as those rings in which the adic and the symbolic topologies of every ideal of the principal class are linearly equivalent. |
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