251 research outputs found
Tight closure and plus closure in dimension two
We prove that the tight closure and the graded plus closure of a homogeneous
ideal coincide for a two-dimensional N-graded domain of finite type over the
algebraic closure of a finite field. This answers in this case a ``tantalizing
question'' of Hochster.Comment: Some minor changes. To appear in Amer. J. of Mat
Lifting chains of prime ideals
We give an elementary proof that for a ring homomorphism A -> B, satisfying
the property that every ideal in A is contracted from B, the following property
holds: for every chain of prime ideals p_0 \subset ... \subset p_r in A there
exists a chain of prime ideals q_0 \subset ... \subset q_r in B such that q_i
\cap A = p_i.Comment: to appear in Journal of pure and applied algebr
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