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Results tagged with ac.commutative-algebra
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user 402
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
1
vote
Accepted
Spectral theorem for unital $C^{*}$-algebras
To see that (1) continues to hold when B is replaced by A,
it suffices (by linearity and density of step functions) to consider only the case when g is the characteristic function of some measurable s …
- 37.8k
7
votes
Is the Pierce spectrum useful elsewhere in Mathematics?
For Boolean rings, the Pierce spectrum coincides with the Zariski spectrum
and is one of the functors implementing the
Stone duality between Boolean algebras and compact
totally disconnected Hausdorff …
- 37.8k
1
vote
How to compute cup product of derived limits / presheaf cohomology
Cup products in sheaf (and presheaf) cohomology are often easy to compute by resolving the source (in the projective model structure, say), not the target.
For an example of resolving the source in th …
- 37.8k
2
votes
Accepted
Categorical Kähler differentials and the Leibniz rule
1. The Leibniz rule follows immediately from the last description
of derivations as morphisms of commutative rings X:R→u(M).
Indeed, u(M) is the square-zero extension of some R-module M'
(in the trad …
- 37.8k
3
votes
1
answer
222
views
Can elements of Weil algebras be detected by maps into truncated symmetric algebras?
Recall that a Weil algebra is a finite-dimensional real unital algebra that admits exactly one homomorphism to R.
Such algebras form the basis of the Weil approach to differential geometry, pioneered …
- 37.8k
16
votes
Accepted
Is there a relation between Gelfand duality and the spectrum of a ring (with its Zariski top...
Yes, both Theorem A and Theorem B are special cases of a more general construction.
Denote by $R$ the category of commutative unital C*-algebras or the category of commutative rings.
Denote by $R'$ th …
- 37.8k