On monomial orders, Koszul algebras and toric rings
This dissertation is concerned with algebraic objects related to, or defined by, monomials, such as monomial orders, toric rings and piecewise lex ideals. The main results include the fact that for any 'n' there exist monomial orders that are not uniquely defined by their induced orders; the fact that the multi-Rees algebra of the direct sum of principal strongly stable ideals is a Koszul Cohen-Macaulay normal domain, if the generating monomials satisfy an ordering property; and a property of piecewise lex ideals.
Caviglia, Purdue University.
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