Math Thesis Archive

Home Personnel Programs Jobs Computing Organization Information Research menubar


ABSTRACT OF THE DISSERTATION

Affine rings of low GK dimension

by

Jason Pierre Bell

We consider algebras of low GK dimension. We give a new, completely combinatorial proof that a finitely generated domain of GK dimension 1 must be a finite module over its center (Theorem 2.4.2). We also show that the monic localization of a polynomial ring over a left Noetherian ring is a Jacobson ring (Theorem 2.3.28). We show that any subfield of the quotient ring of a finitely graded non-PI Goldie algebra of GK dimension 2 over a field F must have transcendence degree at most 1 over F (Theorem 3.3.19). In the fourth chapter we give counter-examples to several questions in ring theory. We construct a prime affine algebra of GK dimension 2 that is neither primitive nor PI; we construct a prime affine algebra of GK dimension 3 that has non-nil Jacobson radical; and we construct a primitve affine algebra of GK dimension 3 with center that is not a field;


Home | Personnel | Programs |Jobs | Computing | Organization | Department | Research