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Let be an abelian group, let be a commutative ring , . and let be is a an left multiplicative - -module if it comes with an-action on and abelian group homomorphism . and be a right multiplicative -action on . is a left -module if is a bilinear function, and is a right -module if is a bilinear function.
Every abelian group is a left-module and a right -module.