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Tag Archives: maximal ideals
Commutative Algebra 14
Basic Open Sets For , let , an open subset of Spec A. Note that . Proposition 1. The collection of over all forms a basis for the topology of . Proof Let be an open subset of Spec A. Suppose … Continue reading
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 11
Coordinate Rings as kalgebras Let k be an algebraically closed field. Recall that a closed subset is identified by its coordinate ring k[V], which is a finitely generated kalgebra since Definition. An affine kvariety is a finitely generated kalgebra A which is … Continue reading
Posted in Advanced Algebra
Tagged algebraic geometry, algebras, cotangent spaces, maximal ideals, tangent spaces, varieties
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Introduction to Ring Theory (5)
Our first order of the day is to state the correspondence between the ideals and subrings of R/I and those of R. This is totally analogous to the case of groups. Theorem. Let I be an ideal of R. There are 11 … Continue reading
Posted in Notes
Tagged advanced, chinese remainder theorem, ideals, maximal ideals, prime ideals, ring theory, rings
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