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yoyostein88
 Post subject: Basic Free Module Question
PostPosted: Thu, 5 Apr 2012 08:22:25 UTC 
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Is the regular R-module R free?

I was thinking, yes, since $R=R^1$.

Thanks for the confirmation.
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Shadow
 Post subject: Re: Basic Free Module Question
PostPosted: Thu, 5 Apr 2012 16:31:14 UTC 
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yoyostein88 wrote:
Is the regular R-module R free?

I was thinking, yes, since $R=R^1$.

Thanks for the confirmation.


Do your rings have a 1?

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yoyostein88
 Post subject: Re: Basic Free Module Question
PostPosted: Fri, 6 Apr 2012 13:19:38 UTC 
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Yes, I am considering rings with 1.
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Shadow
 Post subject: Re: Basic Free Module Question
PostPosted: Fri, 6 Apr 2012 17:20:07 UTC 
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yoyostein88 wrote:
Yes, I am considering rings with 1.


Then yes, R is a free R-module, the basis is composed of the element 1.

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