dc.contributor.advisor | Smalø, Sverre Olaf | nb_NO |
dc.contributor.advisor | Jensen, Bernt Tore | nb_NO |
dc.contributor.author | Nornes, Nils Melvær | nb_NO |
dc.date.accessioned | 2014-12-19T13:57:56Z | |
dc.date.available | 2014-12-19T13:57:56Z | |
dc.date.created | 2010-09-04 | nb_NO |
dc.date.issued | 2008 | nb_NO |
dc.identifier | 348609 | nb_NO |
dc.identifier | ntnudaim:3726 | nb_NO |
dc.identifier.uri | http://hdl.handle.net/11250/258421 | |
dc.description.abstract | In this paper we investigate some partial orders used in representation theory of algebras. Let $K$ be a commutative ring, $Lambda$ a finitely generated $K$-algebra and $d$ a natural number. We then study partial orders on the set of isomorphism classes of $Lambda$-modules of length $d$. The orders degeneration, virtual degeneration and hom-order are discussed. The main purpose of the paper is to study the relation $leq_n$ constructed by considering the ranks of $ntimes n$-matrices over $Lambda$ as $K$-endomorphisms on $M^n$ for a $Lambda$-module $M$. We write $Mleq_n N$ when for any $ntimes n$-matrix the rank with respect to $M$ is greater than or equal to the rank with respect to $N$. We study these relations for various algebras and determine when $leq_n$ is a partial order. | nb_NO |
dc.language | eng | nb_NO |
dc.publisher | Institutt for matematiske fag | nb_NO |
dc.subject | ntnudaim | no_NO |
dc.subject | MMA matematikk | no_NO |
dc.subject | Algebra | no_NO |
dc.title | Partial Orders in Representation Theory of Algebras | nb_NO |
dc.type | Master thesis | nb_NO |
dc.source.pagenumber | 31 | nb_NO |
dc.contributor.department | Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag | nb_NO |