- #1

cbarker1

Gold Member

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Dear Everyone,

I am having trouble with an exercise problem. Here is the problem: Dummit and Foote Ed.2 pg 231: "Let $R$ be a ring with 1. Prove that if $u$ is a unit in R then so is $-u$."

My Attempt:

Suppose $u$ is a unit in $R$. Then, from Prop 1 (4) (if $R$ has an identity, then the identity is unique and $-1a=-a$), let $a=u$. Then $-u$ is in $R$. QED

What did I do wrong and/or correct? Thanks,

Cbarker1

I am having trouble with an exercise problem. Here is the problem: Dummit and Foote Ed.2 pg 231: "Let $R$ be a ring with 1. Prove that if $u$ is a unit in R then so is $-u$."

My Attempt:

Suppose $u$ is a unit in $R$. Then, from Prop 1 (4) (if $R$ has an identity, then the identity is unique and $-1a=-a$), let $a=u$. Then $-u$ is in $R$. QED

What did I do wrong and/or correct? Thanks,

Cbarker1

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