p. 97 - 102 Two-generated ideals of linear type H. Kulosman 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |