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 ^*V and V^* denote the left and right duals we find conditions under which (V^i*,V^(i+1)*,V^(i+2)* ) 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>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Grantor dc:publisher

University of Montana

Year

2009

Author dc:creator

• Hart, John Walker

• Simple
• Rank
• Two-sided

Repository record dc:identifier

https://scholarworks.umt.edu/etd/885

OAI identifier oai:identifier

oai:scholarworks.umt.edu:etd-1904