Exact functor

Homological Algebra
Post Reply
Papapetros Vaggelis
Community Team
Posts: 426
Joined: Mon Nov 09, 2015 1:52 pm

Exact functor

#1

Post by Papapetros Vaggelis »

Let \(\displaystyle{S}\) be a multiplicative subset of the ring \(\displaystyle{A}\) and let \(\displaystyle{M}\)

be an \(\displaystyle{A}\) - module.

The functor \(\displaystyle{M\rightsquigarrow S^{-1}\,M}\) is exact. In other words, if the sequence of \(\displaystyle{A}\) - modules

\(\displaystyle{M' \xrightarrow{f} M \xrightarrow {g} M''}\) is exact, then so also is the sequence of

\(\displaystyle{S^{-1}\,A}\) - modules

\(\displaystyle{S^{-1}\,M' \xrightarrow{S^{-1}\,f} S^{-1}\,M \xrightarrow {S^{-1}\,g} S^{-1}\,M''}\)
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 2 guests