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A.Magnus
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< Mentor Note -- thread moved to HH from the technical math forums >
My final assignment in graduate algebra is to write an essay about the relationship among the subjects we have learned so far this semester:
(1) Module
(2) The Field of Fractions of an Integral Domain
(3) Integrality
(4) Integrality and Fields
(5) Prime Ideals
(6) The Krull Dimension
(7) Noetherian Modules
(8) Noetherian Integral Domain
(9) Dedekind Domain
I know they belong to the Commutative Algebra, but here is my problem: My present math maturity level is capable of seeing only the nuts and bolts of those subjects, but not the whole overall picture. I would appreciate if somebody out there gives me the ideas about the big picture, their inter-connection, or any online resources that I can turn to.
Thank you very much for your time and help.
My final assignment in graduate algebra is to write an essay about the relationship among the subjects we have learned so far this semester:
(1) Module
(2) The Field of Fractions of an Integral Domain
(3) Integrality
(4) Integrality and Fields
(5) Prime Ideals
(6) The Krull Dimension
(7) Noetherian Modules
(8) Noetherian Integral Domain
(9) Dedekind Domain
I know they belong to the Commutative Algebra, but here is my problem: My present math maturity level is capable of seeing only the nuts and bolts of those subjects, but not the whole overall picture. I would appreciate if somebody out there gives me the ideas about the big picture, their inter-connection, or any online resources that I can turn to.
Thank you very much for your time and help.
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