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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. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   2. In geometry and linear algebra, denotes the cross product. 3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3.

4. Basis (universal algebra) - Wikipedia

   en.wikipedia.org/wiki/Basis_(universal_algebra)

   In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras.It generates all algebra elements from its own elements by the algebra operations in an independent manner.

5. Transcendental number theory - Wikipedia

   en.wikipedia.org/wiki/Transcendental_number_theory

   Free algebra. Clifford algebra • Geometric algebra Operator algebra. Transcendental number theory is a branch of number theory that investigates transcendental ...

6. 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 ...

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8. Free product of associative algebras - Wikipedia

   en.wikipedia.org/wiki/Free_product_of...

   In algebra, the free product of a family of associative algebras, over a commutative ring R is the associative algebra over R that is, roughly, defined by the generators and the relations of the 's. The free product of two algebras A, B is denoted by A ∗ B.

9. Cheat sheet - Wikipedia

   en.wikipedia.org/wiki/Cheat_sheet

   A cheat sheet that is used contrary to the rules of an exam may need to be small enough to conceal in the palm of the hand Cheat sheet in front of a juice box. A cheat sheet (also cheatsheet) or crib sheet is a concise set of notes used for quick reference. Cheat sheets were historically used by students without an instructor or teacher's ...