On Noetherian Rees algebras and symbolic powers

Adam Alexander Hill, Tennessee State University


My research explores the relationship of Noetherian Rees algebras and symbolic powers. Cowsik proposed a question: if R is a regular local ring and p ⊂ R is a prime ideal, then is ⊕ n≥0 p&parl0;n&parr0;tn Noetherian? We call Rs( p ) = ⊕n≥0 p&parl0;n&parr0;tn , the symbolic Rees algebra of p . This research is based on the findings of Craig Huneke, a mathematics professor at the University of Kansas, who hoped to answer a question provided by Cowsik. It has been unknown for several years whether Rs( p ) is Noetherian for prime ideals defining monomial curves until Huneke's discoveries. Huneke developed criteria for when the symbolic Rees algebra is Noetherian for certain primes defining these monomial curves. He showed us that Rs( p ) is Noetherian for all primes defining monomial curves as long as the multiplicity of R/ p is less than or equal to four. In this paper, we are going to further explore Huneke's theories for multiplicity five for these stated monomial curves. ^

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Recommended Citation

Adam Alexander Hill, "On Noetherian Rees algebras and symbolic powers" (2008). ETD Collection for Tennessee State University. Paper AAI1456758.