Separable Algebra

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 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 ...

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