Algebraic geometry is heavily dependent on commutative algebra, the study of commutative rings and fields (notably those arising from polynomial rings in many variables); indeed, it is impossible to draw a sharp line between the geometry and the algebra. For reference, we assemble in this section some basic concepts and results (without proof) of an algebraic nature. The theorems stated are in most cases “standard” and readily accessible in the literature, though not always encountered in a graduate algebra course.
KeywordsPrime Ideal Irreducible Component Local Ring Projective Variety Valuation Ring
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