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Two-generated ideals of linear type
Received: January 6, 2008; Revised: June 16, 2008; Accepted: June 30, 2008
Abstract. We show that in a local S1 ring every two-generated ideal of linear type can be generated by a two-element sequence of linear type and give an example which illustrates that the S1 condition is essential. We also show that every Noetherian local ring in which every two-element sequence is of linear type is an integrally closed integral domain and every two generated ideal of it can be generated by a two-element d-sequence. Finally, we investigate two-element c-sequences and characterize them under some mild assumptions.
Keywords: ideal of linear type; sequence of linear type; d-sequence; c-sequence.
AMS Subject classification: Primary: 13A30, 13B22, 13B25 Secondary: 13E15
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