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arXiv · 1811.06380

Embeddings of Free Magmas with Applications to the Study of Free Non-Associative Algebras

Cameron Ismail
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Abstract

We introduce an embedding of the free magma on a set A into the direct product of the free magma on a singleton set and the free semigroup on A. This embedding is then used to prove several theorems related to algebraic independence of subsets of the free non-associative algebra on A. Among these theorems is a generalization of a result due to Kurosh, which states that every subalgebra of a free non-associative algebra is also free.

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Cameron Ismail. 2018-11-15. Embeddings of Free Magmas with Applications to the Study of Free Non-Associative Algebras. https://arxiv.org/abs/1811.06380

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