Paper Information

Title: 

CLEANNESS AND SHELLABLITY

Type: PAPER
Author(s): SOLEYMAN JAHAN ALI*
 
 *DEPARTMENT OF MATHEMATICS, UNIVERSITY OF KURDISTAN 416, SANANDAJ, IRAN
 
Name of Seminar: SEMINAR ON ALGEBRA (SALG20)
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

We study some basic property of cleanness. We show that if R is a Notherian ring and M is an almost clean R-module with the property that R/P is Cohen–Macaulay for any PÎAss(M), then depth (M)=min{dim(R/P) : pÎAss(M)}. Using this fact show that if M is a clean R-module and all minimal prime ideals of M are Cohen–Macaulay and have equal height, then M is Cohen–Macaulay. We also discuss the relation between cleanness and shalleblity and give a simple proof for a theorem of Dress. Finally we give an easy proof for the well known fact that a pure shellable simplicial complex is Cohen–Macaulay.

 
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