Re: Projective envelope

From: Jannick Asmus (jannick.news_at_web.de)
Date: 02/19/05 

Date: Sat, 19 Feb 2005 09:41:17 +0100

On 19.02.2005 05:11, Paul Sperry wrote:

>>Is there such a thing as projective envelope of a left R-module M? I know
>>that an injective envelope of an R-module M exists, where injective envelope
>>means an injective R-module that is also an essential extension of M. But
>>is there an analog for projective envelopes? I searched on google and
>>didn't really find anything.
>
>
> Google "projective cover".
>

Tony,

Paul is right in saying that there is some projective module above M,
i.e. there is a projective module P and a _surjection_ P ->> M (or: the
is an exact sequence P -> M -> 0).

Basically the notion of 'injective' and 'projective' are 'dual' to each
other. By this I mean -and I am simplyfying here- that switching
between the notions the direction of the arrows are reversed.

J.

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