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Classification of almost monomial subalgebras of small codimension

Sundell, Ludvig LU (2023) In Bachelor's Theses in Mathematical Sciences MATK11 20231
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
In this text, we study almost monomial subalgebras using LAGBI bases. We
introduce the concept of a LAGBI base and present an algorithm for computing
them. We then use this algorithm to find, and present in a table, all polynomial
subalgebras with Frobenius number smaller than or equal to ten. We then prove
that some patterns observed in this table hold. Lastly we give a proof of what
properties isomorphic subalgebras must have and use this to find all polynomial
subalgebras up to isomorphism with Frobenius number up to five.
Popular Abstract (Swedish)
Inom matematiken är det ofta intressant att studera olika strukturer, deras
egenskaper, och hur man bäst representerar dem. Så kallade ideal av ringar är
ett välstuderat område, men en liknande klass av strukturer kallad subalgebror
är hittills mindre studerade. I denna text ges grundläggande definitioner och
satser relaterat till LAGBI baser som sedan används för att klassificera vissa
polynomsubalgebror med liten kodimension.
Please use this url to cite or link to this publication:
author
Sundell, Ludvig LU
supervisor
organization
course
MATK11 20231
year
type
M2 - Bachelor Degree
subject
keywords
Algebra, Subalgebra, Polynomial, SAGBI basis, LAGBI basis, Lower semigroup
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUNFMA-4146-2023
ISSN
1654-6229
other publication id
2023:K16
language
English
id
9130899
date added to LUP
2023-07-05 15:50:20
date last changed
2023-07-05 15:50:20
@misc{9130899,
  abstract     = {{In this text, we study almost monomial subalgebras using LAGBI bases. We
introduce the concept of a LAGBI base and present an algorithm for computing
them. We then use this algorithm to find, and present in a table, all polynomial
subalgebras with Frobenius number smaller than or equal to ten. We then prove
that some patterns observed in this table hold. Lastly we give a proof of what
properties isomorphic subalgebras must have and use this to find all polynomial
subalgebras up to isomorphism with Frobenius number up to five.}},
  author       = {{Sundell, Ludvig}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{Classification of almost monomial subalgebras of small codimension}},
  year         = {{2023}},
}