CLEANNESS AND SHELLABLITY

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SOLEYMAN JAHAN ALI

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Seminar Paper

Paper Information

Seminar: IRANIAN ALGEBRA SEMINAR
Year:2009 | Issue:20

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Information Seminar Paper

Title

CLEANNESS AND SHELLABLITY

Author(s)

SOLEYMAN JAHAN ALI

Keywords

Not Registered.

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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Cite

APA: Copy

SOLEYMAN JAHAN, ALI. (2009). CLEANNESS AND SHELLABLITY. IRANIAN ALGEBRA SEMINAR. SID. https://sid.ir/paper/904404/en

Vancouver: Copy

SOLEYMAN JAHAN ALI. CLEANNESS AND SHELLABLITY. 2009. Available from: https://sid.ir/paper/904404/en

IEEE: Copy

ALI SOLEYMAN JAHAN, “CLEANNESS AND SHELLABLITY,” presented at the IRANIAN ALGEBRA SEMINAR. 2009, [Online]. Available: https://sid.ir/paper/904404/en

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