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[Music] welcome this is lecture 55. so in uh in the next this lecture and the next five we will look at ccgs called free resolutions and uh what information can be uh cleaned out of computing free resolutions okay sorry some information that can be gleaned out of there are many other things that can be obtained by looking at a free resolution we will see an introduction to that so so we are discussing were going to start free resolutions so we will not be able to prove many things properly because uh to to discuss these things one needs to spend some time developing basic notions about complexes and homological algebra which we have not done and we do not have the time now to do this so there will be a few results that we will assume and then we will see how to use them or how what okay so recall so i have not yet defined this but lets so recall that okay so if you have an ideal i inside a polynomial ring [Music] k adjoined some n variables okay then when we only looked at this case
