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  2. Free algebra - Wikipedia

    en.wikipedia.org/wiki/Free_algebra

    Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.

  3. Tensor algebra - Wikipedia

    en.wikipedia.org/wiki/Tensor_algebra

    In mathematics, the tensor algebra of a vector space V, denoted T(V) or T • (V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product.It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property ...

  4. List of open-source software for mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_open-source...

    This was the case until in 1997 when they decided to co-develop GAP further with CIRCA (Centre for Research in Computational Algebra). Unlike MAXIMA and Axiom, GAP is a system for computational discrete algebra with particular emphasis on computational group theory. In March 2005 the GAP Council and the GAP developers have agreed that status ...

  5. Algebraic structure - Wikipedia

    en.wikipedia.org/wiki/Algebraic_structure

    An algebraic structure in a variety may be understood as the quotient algebra of term algebra (also called "absolutely free algebra") divided by the equivalence relations generated by a set of identities. So, a collection of functions with given signatures generate a free algebra, the term algebra T.

  6. Free object - Wikipedia

    en.wikipedia.org/wiki/Free_object

    In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.

  7. The Term Sheet handoff - AOL

    www.aol.com/finance/term-sheet-handoff-121214752...

    Term Sheet has been the cornerstone of my life these past two years, and your willingness to let me into yours has been an honor. I’m not going off into the sunset entirely.

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