Nonassociative structures on polynomial algebras arising from bio-operations on formal languages: an application of computer algebra to nonassociative systems
Pages 41 - 48
Abstract
We consider sequential insertion and deletion, and contextual insertion and deletion, on the free monoid Σ where Σ = {x}; in each case the result can be regarded as either a set or a multiset. Over any coefficient field F the vector space with basis Σ* is linearly isomorphic to the polynomial algebra F[x]; each operation on Σ* extends bilinearly to give a new algebra structure (not necessarily commutative or associative) on F[x]. We determine the polynomial identities of degree ≤ 5 satisfied by these structures.
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Index Terms
- Nonassociative structures on polynomial algebras arising from bio-operations on formal languages: an application of computer algebra to nonassociative systems
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Published: 29 July 2007
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ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada
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