Vol. 36, No. 2, 1971

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ISSN: 0030-8730
Regular sequences and minimal bases

Edward Dewey Davis

Vol. 36 (1971), No. 2, 323–326

This note records the results of an effort to understand in simple terms a certain theorem of Lichtenbaum and Schlessinger: Let I J be ideals of noetherian local ring. If I and I∕J are generated by regular sequences, then so is J. This theorem is closely related to the well known: If R and R∕P are regular local rings, then P is generated by part of a regular system of parameters. We investigate the implications of “I∕J is generated by a regular sequence” and discover an elementary theorem having both of these results as corollaries.

Mathematical Subject Classification
Primary: 13.95
Received: 16 March 1970
Published: 1 February 1971
Edward Dewey Davis