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Description of Single Cluster Subalgebras

Kennerland, Erik LU (2024) In Master's Theses in Mathematical Sciences FMAM05 20242
Mathematics (Faculty of Engineering)
Abstract
For unital and commutative algebras over an algebraically closed field, any inclusion of finite codimension can be characterised as a chain of inclusions of codimension 1. We investigate the behaviour of such chains when the said algebras are ideal subalgebras. That is, when they are sums of the base field with an ideal. So called single clustered polynomial subalgebras can be guaranteed to be contained in a particular type of ideal subalgebra and we provide a means to determine their structure. This characterisation is a direct generalisation of previous results on so called almost monomial subalgebras.
Popular Abstract
A polynomial subalgebra consists of polynomials which can be added and multiplied. Often, the structure of a subalgebra is difficult to understand, but many times it is possible to find a list of easily described conditions to determine whether a polynomial is part of an algebra or not. We propose a method of finding these conditions for a special type called single clustered subalgebras. The method is a generalisation of solving the same problem on so called zero spectrum subalgebras.
Please use this url to cite or link to this publication:
author
Kennerland, Erik LU
supervisor
organization
course
FMAM05 20242
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Derivation, Devaluation, Ideal Subalgebra, Multispectrum, Subalgebra Conditions, Subalgebra Spectrum
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMA-3561-2024
ISSN
1404-6342
other publication id
2024:E77
language
English
id
9184144
date added to LUP
2025-07-01 11:42:19
date last changed
2025-07-01 13:09:24
@misc{9184144,
  abstract     = {{For unital and commutative algebras over an algebraically closed field, any inclusion of finite codimension can be characterised as a chain of inclusions of codimension 1. We investigate the behaviour of such chains when the said algebras are ideal subalgebras. That is, when they are sums of the base field with an ideal. So called single clustered polynomial subalgebras can be guaranteed to be contained in a particular type of ideal subalgebra and we provide a means to determine their structure. This characterisation is a direct generalisation of previous results on so called almost monomial subalgebras.}},
  author       = {{Kennerland, Erik}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Description of Single Cluster Subalgebras}},
  year         = {{2024}},
}