ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Vol. LXXVIII, 1 (2009)
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






Acta Mathematica Universitatis Comenianae
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