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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
4
votes
Are all ideals $I$ in the ring of smooth functions on a compact manifold M equal to a set of...
I realize that this is an old question, but it was never answered here. So I'll take a crack at it: no, not every ideal is of the form $\frak{m}\!$$_Z$.
Let $M$ be a compact Hausdorff manifold. Then ( …