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Information Seminar Paper

Title

VANISHING AND ARTINIANNESS OF LOCAL COHOMOLOGY MODULES

Writers

VAHIDI ALIREZA

Pages

 Start Page | End Page

Abstract

 LET R BE A COMMUTATIVE NOETHERIAN RING WITH NON-ZERO IDENTITY, A AN IDEAL OF R, AND X AN ARBITRARY R–MODULE. IN THIS PAPER, FOR FIXED NON-NEGATIVE INTEGERS S, T AND A FINITE A–TORSION R–MODULE N, WE FIRST STUDY THE MEMBERSHIP OF TOR RS (N,HTA (X)) IN SERRE SUBCATEGORIES OF THE CATEGORY OF R–MODULES. THEN WE SHOW THAT, FOR CERTAIN INTEGER I, HIA(X) MAY NOT BE FINITE, COATOMIC, OR MINIMAX. FINALLY, FOR A POSITIVE INTEGER N, WE FIND SOME EQUIVALENT STATEMENTS FOR “HIA(X) = 0 FOR ALL I ³ N” AND “HIA(X) IS ARTINIAN FOR ALL I ³ N”.

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