scholarly journals On the Depth of the Associated Graded Ring of an Ideal

2002 ◽  
Vol 248 (2) ◽  
pp. 688-707 ◽  
Author(s):  
Laura Ghezzi
Keyword(s):  
Associated Graded Ring ◽  
Graded Ring

On the Buchsbaumness of the Associated Graded Ring of a One-Dimensional Local Ring

2009 ◽  
Vol 37 (5) ◽  
pp. 1594-1603 ◽  
Author(s):  
M. D'Anna ◽  
M. Mezzasalma ◽  
V. Micale
Keyword(s):  
Local Ring ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
One Dimensional

scholarly journals The depth of the associated graded ring of ideals with any reduction number

2004 ◽  
Vol 276 (1) ◽  
pp. 168-179 ◽  
Author(s):  
Ian Aberbach ◽  
Laura Ghezzi ◽  
Huy Tài Hà
Keyword(s):  
Associated Graded Ring ◽  
Graded Ring ◽  
Reduction Number

scholarly journals Quasi-socle ideals in Buchsbaum rings

2010 ◽  
Vol 200 ◽  
pp. 93-106
Author(s):  
Shiro Goto ◽  
Jun Horiuchi ◽  
Hideto Sakurai
Keyword(s):  
Local Ring ◽  
Associated Graded Ring ◽  
Graded Ring

AbstractQuasi-socle ideals, that is, ideals of the formI = Q: mq(q≥ 2), withQparameter ideals in a Buchsbaum local ring (A,m), are explored in connection to the question of whenIis integral overQand when the associated graded ring G(I) ⊕n≥0In/In+1ofIis Buchsbaum. The assertions obtained by Wang in the Cohen-Macaulay case hold true after necessary modifications of the conditions on parameter idealsQand integersq. Examples are explored.

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