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Algebra 2 Takehome Final
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Due Wednesday May 2, 2012
Construct an example of a pair (R,P) such that R is an integral domain
and P is a projective R-module but not a free R-module.
Then write a short expository paper about your construction, including
a proof that it satisfies the requirement.
(I hope that this can be done in 3-4 pages, but there are no
requirements on the length.)
You are welcome to speak to others or consult the literature to solve
the problem, but your paper should be written individually.
In general, paper has (at least) the following components:
1) A title, a list of authors, and a date.
2) An introduction.
3) The body of the paper.
4) A list of references.
The introduction has two main goals: a) Make your readers interested
in the subject, and b) briefly explain the history of the subject and
how your new paper fits in there.
For a) you might explain the "big picture", state main results,
mention applications and relationships with other parts of
mathematics. And of course, if your paper introduces new and
revolutionary results or methods, then explain the great benefits to
humanity resulting from this! Part b) includes mentioning earlier
work on the same subject. In particular, if parts of your results,
methods, or proofs etc. have appeared earlier, then point this out,
stating where it can be found. A good and interesting account of the
history can also greatly amplify the reader's interest.
The body of the paper does the actual work, state definitions, prove
theorems, give examples, etc.
How all of this applies to your expository paper on projective modules
is up to you.
Anders