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SIMPLE TWO-SIDED RATIONAL VECTOR SPACES OF RANK TWO

<p>The purpose of this thesis is to find sufficient conditions under which a non-commutative version of the polynomial ring in two variables exists. The non-commutative rings we construct are non-commutative symmetric algebras over a two-sided vector space. After reviewing the definition of a two-sided vector space and giving some examples, we briefly recall the theory of simple two-sided vector spaces. We then assume k is a field of characteristic zero and t is transcendental over k and we find sufficient conditions under which a simple k-central two-sided vector space V over k(t) has left and right dimension two. Given such a V, and letting <sup>*</sup>V and V<sup>*</sup> denote the left and right duals we find conditions under which (V<sup>i*</sup>,V<sup>(i+1)*</sup>,V<sup>(i+2)*</sup> ) has a simultaneous for all i, i an integer. This condition implies the non-commutative symmetric algebra over V can be constructed. We conclude by exhibiting a five-dimensional family of simple k-central two-sided vector spaces over k(t) of left and right dimension two who non-commutative symmetric algebras exist.</p>

Identiferoai:union.ndltd.org:MONTANA/oai:etd.lib.umt.edu:etd-03102010-094108
Date25 March 2010
CreatorsHart, John Walker
ContributorsAdam Nyman, Nikolaus Vonessen, Jennifer Halfpap, George McRae, Andrew Ware
PublisherThe University of Montana
Source SetsUniversity of Montana Missoula
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.umt.edu/theses/available/etd-03102010-094108/
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