Summary
Let k be a field, k′ an algebraic extension field, X 1 , ..., Xn indeterminates, A an ideal in k[X 1 , ..., Xn], and let A′ = k[X 1 , ..., Xn]A. It is shown that any associated prime of A′ contracts in k[X 1 , ..., Xn] to an associated prime of A. Some other old questions of Krull are also answered.
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To Professor BeniaminoSegre on his seventieth birthday
Entrata in Redazione il 7 maggio 1973.
Supported in part by an N.S.F. grant. Written in Rome, Italy, Summer 1972.
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Seidenberg, A. The prime ideals of a polynomial ideal under extension of the base field. Annali di Matematica 102, 57–59 (1975). https://doi.org/10.1007/BF02410595
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DOI: https://doi.org/10.1007/BF02410595