Free Algebras
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Ismail, Cameron Ford
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Abstract
In this thesis, we develop a useful framework for studying the free (nonassociative) algebra on a set. This framework will be used to prove several results regarding subalgebras of a free algebra and quotient algebras of a free algebra by an ideal. In particular, we prove a result known as Kurosh's Theorem which, informally speaking, states that "every subalgebra of a free (nonassociative) algebra is free". During this process, we also develop a framework for studying the free magma on a set.