In mathematics, a **separable algebra** is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension.

Read more about Separable Algebra: Definition and First Properties, Commutative Separable Algebras, Examples, Separable Extensions For Noncommutative Rings

### Other articles related to "separable algebra, algebra, separable, algebras":

**Separable Algebra**- Separable Extensions For Noncommutative Rings

... Notice that an R-R-bimodule (see module theory and homological

**algebra**) restricts to an S-S-bimodule ... The ring extension R over S is said to be a

**separable**extension if all short exact sequences of R-R-bimodules that are split as R-S-bimodules also split as R-R-bimodules ... If R is a

**separable**extension over S, then the multiplication mapping is split as an R-R-bimodule epi, so there is a right inverse s of m satisfying for s(1) = e, re ...

Hopf Algebras - Related Concepts

... Graded Hopf

... Graded Hopf

**algebras**are often used in algebraic topology they are the natural algebraic structure on the direct sum of all homology or cohomology groups of an H-space ... Locally compact quantum groups generalize Hopf**algebras**and carry a topology ... The**algebra**of all continuous functions on a Lie group is a locally compact quantum group ...### Famous quotes containing the word algebra:

“Poetry has become the higher *algebra* of metaphors.”

—José Ortega Y Gasset (1883–1955)

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