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Abstract Algebra

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Modules Scalar Multiplications

ABSALG-VWLG68

Let $R$ be a commutative ring with unity. We know that there are several ways to make $R$ a module over itself.

Which of the following scalar multiplication make $R$ a module over itself? Select ALL that apply.

A

$(a,b)\mapsto 0$

B

$(a,b)\mapsto ab$

C

$(a,b)\mapsto a+b$

D

$(a,b)\mapsto a$

E

$(a,b)\mapsto b$