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Tag Archives: zariski topology
Commutative Algebra 13
Zariski Topology for Rings In this article, we generalize earlier results in algebraic geometry to apply to general rings. Recall that points on an affine variety V correspond to maximal ideals . For general rings, we have to switch to … Continue reading
Posted in Advanced Algebra
Tagged homomorphism, maximal ideals, prime ideals, rings, spectrum, topology, zariski topology
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Commutative Algebra 4
More Concepts in Algebraic Geometry Recall that we have a bijection between radical ideals of and closed subsets of . The bijection reverses the inclusion so if and only if . Not too surprisingly, operations on ideals translate to operations … Continue reading
Posted in Advanced Algebra
Tagged algebraic geometry, closed subsets, ideals, irreducible spaces, rings, zariski topology
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Commutative Algebra 3
Algebraic Geometry Concepts We have decided to introduce, at this early point, some basics of algebraic geometry in order to motivate the later concepts. In summary, algebraic geometry studies solutions to polynomial equations over a field. First we consider a … Continue reading
Posted in Advanced Algebra
Tagged algebraic geometry, commutative rings, ideals, nullstellensatz, radical ideals, rings, topology, zariski topology
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