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dc.contributor.authorBiermann, Jenniferen_US
dc.identifier.otherbibid: 7955485
dc.description.abstractLet k be a field and S = k [x1 , . . . , xn ] a polynomial ring. This thesis considers the structure of minmial free resolutions of monomial ideals in S . In Chapter 3 we study reverse lex ideals, and compare their properties to those of lex ideals. In particular we provide an analogue of Green's Theorem for reverse lex ideals. We also compare the Betti numbers of strongly stable and square-free strongly stable monomial ideals to those of reverse lex ideals. In Chapter 5 we study the minimal free resolution of the edge ideal of the complement of the n-cycle for n [GREATER-THAN OR EQUAL TO] 4 and construct a regular cellular complex which supports this resolution.en_US
dc.subjectCommutative Algebraen_US
dc.subjectMonomial idealsen_US
dc.subjectFree resolutionsen_US
dc.titleFree Resolutions Of Monomial Idealsen_US
dc.typedissertation or thesisen_US Universityen_US of Philosophy D., Mathematics
dc.contributor.chairPeeva, Irena Vassilevaen_US
dc.contributor.committeeMemberSwartz, Edward B.en_US
dc.contributor.committeeMemberStillman, Michael Eugeneen_US

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