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What are the contents of commutative algebra 00ao?
COMMUTATIVE ALGEBRA Contents COMMUTATIVE ALGEBRA 00AO Contents 1. Introduction 4 2. Conventions 4 3. Basicnotions 5 4. Snakelemma 7 5. Finitemodulesandfinitelypresentedmodules 7 6. Ringmapsoffinitetypeandoffinitepresentation 9 7. Finiteringmaps 10 8. Colimits 11 9. Localization 14 10. InternalHom 19 11.
Which construction arises frequently in commutative algebra?
A construction that arises frequently in commutative algebra is the colon ideal. We give the de nition here. Let I R be an ideal in the ring R, and let S be an arbitrary subset of R. Then I :R S (or simply I : S) is, by de nition, fr 2 R : for all s 2 S; rs 2 Ig, which is easily veri ed to be an ideal of R. If
What is commutative algebra 54?
COMMUTATIVE ALGEBRA 54 is thatI=R∩m for some maximal ideal m of the ringS−1R. It turns out that for many properties of ideals, the maximal ones are prime. A general method of seeing this was developed in [LR08]. In this section, we digress to explain this phenomenon. LetRbearing.
Is a commutative ring an A-algebra?
We next want to de ne the notion of an A-algebra, where A is a commutative ring. We shall say that R is an A-algebra if R itself is a commutative ring and is also (unital) A-module in such a way that for all a 2 A and r; s 2 R, a(rs) = (ar)s.

What are the contents of commutative algebra 00ao?