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Commutative Algebra and Algebraic Geometry MATH 441 (3)

A study of ideals and varieties. Topics include affine varieties, ideals, Groebner bases, the Hilbert basis theorem, resultants and elimination, Hilbert's Nullstellensatz. irreducible varieties and prime ideals, decomposition of varieties, polynomial mappings, quotient rings, projective space and projective varieties. Prerequisite: MATH 340. Students who have taken this course as MATH 439 Special Topics may not complete this course for further credit.