Free product of associative algebras

In algebra, the free product (coproduct) of a family of associative algebras A_i, i \in I over a commutative ring R is the associative algebra over R that is, roughly, defined by the generators and the relations of the A_i's. ^[1]

6 relations: Associative algebra, Category of rings, Coproduct, Free product, Tensor algebra, Tensor product of algebras.

Associative algebra

In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.

New!!: Free product of associative algebras and Associative algebra · See more »

Category of rings

In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (preserving the identity).

New!!: Free product of associative algebras and Category of rings · See more »

Coproduct

In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.

New!!: Free product of associative algebras and Coproduct · See more »

Free product

In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “most general” group having these properties.

New!!: Free product of associative algebras and Free product · See more »

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.

New!!: Free product of associative algebras and Tensor algebra · See more »

Tensor product of algebras

In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra.

New!!: Free product of associative algebras and Tensor product of algebras · See more »

Redirects here:

Free product of algebras.

References

[1] https://en.wikipedia.org/wiki/Free_product_of_associative_algebras

Unionpedia is a concept map or semantic network organized like an encyclopedia – dictionary. It gives a brief definition of each concept and its relationships.

This is a giant online mental map that serves as a basis for concept diagrams. It's free to use and each article or document can be downloaded. It's a tool, resource or reference for study, research, education, learning or teaching, that can be used by teachers, educators, pupils or students; for the academic world: for school, primary, secondary, high school, middle, technical degree, college, university, undergraduate, master's or doctoral degrees; for papers, reports, projects, ideas, documentation, surveys, summaries, or thesis. Here is the definition, explanation, description, or the meaning of each significant on which you need information, and a list of their associated concepts as a glossary. Available in English, Spanish, Portuguese, Japanese, Chinese, French, German, Italian, Polish, Dutch, Russian, Arabic, Hindi, Swedish, Ukrainian, Hungarian, Catalan, Czech, Hebrew, Danish, Finnish, Indonesian, Norwegian, Romanian, Turkish, Vietnamese, Korean, Thai, Greek, Bulgarian, Croatian, Slovak, Lithuanian, Filipino, Latvian, Estonian and Slovenian. More languages soon.

All the information was extracted from Wikipedia, and it's available under the Creative Commons Attribution-ShareAlike License.

Unionpedia is not endorsed by or affiliated with the Wikimedia Foundation.

Google Play, Android and the Google Play logo are trademarks of Google Inc.