MATH 368
Positive Characteristic Commutative Algebra Spring 2018 Division III; Quantative/Formal Reasoning;
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In commutative algebra, one of the most basic invariants of a ring is its characteristic. This is the smallest multiple of 1 that equals 0. Working over a ring of characteristic zero, versus a ring of characteristic p>0, dramatically changes the proof techniques available to us. This realization has had tremendous consequences in commutative algebra. One of the most useful tools in characteristic p is the Frobenius homomorphism. In this course we will study several standard notions in commutative algebra, such as regularity of a ring, Cohen-Macaulayness, and being normal and we will see how various “splittings” of the Frobenius allow us to easily detect these properties. Many of these methods are not only applicable to commutative algebra, but also to number theory and algebraic geometry.
The Class: Type: lecture
Limit: 30
Expected: 15
Class#: 3882
Requirements/Evaluation: homework and a final exam
Extra Info: may not be taken on a pass/fail basis; not available for the fifth course option
Prerequisites: MATH 355 or permission of instructor
Enrollment Preference: Math majors primarily, and juniors and seniors secondarily
Distributions: Division III; Quantative/Formal Reasoning;

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