Prime filtrations of modules and Stanley decopositions [Elektronische Ressource] / von Ali Soleyman Jahan

Description

Prime filtrations of modules and StanleydecompositionsDissertation zur Erlangung desDoktorgrades (Dr. rer. nat.)vorgelegt demFachbereich 6Mathematik und Informatikder Universit¨at Duisburg-EssenvonAli Soleyman Jahanaus dem IranMay 2008Vorsitzender: Prof. Dr. Trung Van TranErster Gutachter: Prof. Dr. Ju¨rgen HerzogZweiter Gutachter: Prof. Dr. Ralf Fr¨obergDedicated to my wife, my sons Sina and Siamand and my parents.AcknowledgmentsIamverygratefultomyadvisorProf.Ju¨rgenHerzogforhiscontinuousguidance,tremendous support and encouragement throughout the preparation of my thesis.I also wish to thank Professor Siamak Yassemi and Dr. Xinxian Zheng formathematical discussion that I had with them during our joint papers.IwouldliketothanktheministryofScience, Research andTechnologyofIslamicRepublic of Iran and the University of Kurdistan for the financial support that theyoffered to me during my Ph.D study. Lastly, I thank the University of Essen–Duisdurg for its hospitality and the facilities provided during my Ph.D study andresearch.ContentsPreface 11 Preliminaries 61.1 Graded rings and graded modules . . . . . . . . . . . . . . . . . . . . 61.2 Dimension filtration and Cohen–Macaulay filtration . . . . . . . . . . 81.3 Clean and pretty clean modules . . . . . . . . . . . . . . . . . . . . . 101.4 Simplicial complexes and Stanley–Reisner ring . . . . . . . . . . . . . 121.5 Multicomplexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.

Sujets

• Mathematics

Informations

• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2008
• Nombre de lectures: 12
• Langue: English

Extrait