Year of Award
Dissertation - Campus Access Only
Doctor of Philosophy (PhD)
Department or School/College
Department of Mathematical Sciences
Eric Chesebro, Nikolaus Vonessen, Elizabeth Gillaspy, Oliver Serang
Brauer Group, Central Simple Algebras, Cyclic algebras, Essential Dimension, Kummer Subspaces, Non Commutative Algebra
University of Montana
We separate this dissertation into three distinct but related parts. Chapter one focuses on p-Kummer subspaces of G-crossed products where G is an elementary abelian group. We show that if A is a generic G-crossed product with not strong degenerate u matrix, all p-Kummer subspaces are of dimension 1 over the center. The second chapter makes use of the essential dimension of (Z=pZ)r over a eld of characteristic p. We provide an upper bound of the essential dimension of the functor Decn+1;p` as well as a concrete construction of the eld and algebra of descent for the functor Dec2;pr . Chapter three explores the Galois symbol and related objects. We make use of divided power maps on the the cohomology groups Hn(K; n p ) to provide a lower bound for the functor hn; 'p.
Nguyen, Nhan Trong, "CENTRAL SIMPLE ALGEBRAS AND RELATED OBJECTS IN BOTH ZERO AND POSITIVE CHARACTERISTIC" (2018). Graduate Student Theses, Dissertations, & Professional Papers. 11258.
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