Abstract
On any set X may be defined the free algebra R〈X〉 (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X * (respectively, free commutative monoid . Furthermore, the algebra of differential polynomials R{X} with variables in X may be constructed. The main objective of this contribution is to provide a functorial description of this kind of objects with their relations (including abelianization and unitarization) in the category of differential algebras, and also to introduce new structures such as the differential algebra of a semigroup, of a monoid, or the universal differential envelope of an algebra.
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Poinsot, L. (2014). Differential (Monoid) Algebra and More. In: Barkatou, M., Cluzeau, T., Regensburger, G., Rosenkranz, M. (eds) Algebraic and Algorithmic Aspects of Differential and Integral Operators. AADIOS 2012. Lecture Notes in Computer Science, vol 8372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54479-8_8
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DOI: https://doi.org/10.1007/978-3-642-54479-8_8
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