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Type: Thingyago:KnowledgeDomain105999266yago:PsychologicalFeature100023100yago:Abstraction100002137yago:Algebra106012726yago:Algebrasyago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:Mathematics106000644yago:PureMathematics106003682yago:Science105999797 New Facet based on Instances of this Class

In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.