Math 593 : Problem Set 5 Professor Karen
نویسنده
چکیده
1. Exact sequences A sequence of R-module maps A φ → B π → C is exact if the kernel of π and the image of φ are the exact same submodule of B. A longer sequence is exact by definition if every subsequence of two consecutive maps is exact. a). Show that B π → C → 0 is exact if and only if π is surjective. The kernel of C → 0 is all of C, so it is exact if the image of π is all of C—that is, if π is surjective.
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1 Acknowledgements I would first like to thank my advisor Professor Karen Lange. She has quite literally taught me everything I know about computability. She has helped me develop as not only a math researcher, but also a writer and presenter. I would also like to thank NSF grant DMS-1100604 for funding summer research that was instrumental in helping me complete this thesis. I would also like ...
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