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Results tagged with ra.rings-and-algebras
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user 6153
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.
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cyclic polynomials and their solutions
So you have a cyclic group acting on complex affine space, and the situation at the level of function fields is clear enough: by basic Galois theory the extension of rational functions is a cyclic ext …
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14
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Accepted
When is a ring the ring of adeles of some global field
Iwasawa gave a characterisation, assuming you are given a subfield F, discrete and such that the quotient is compact. The other conditions are R a semisimple locally compact commutative topological ri …
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Rank of sum of Galois conjugates of a matrix
You can do this: take a normal basis for K, and write M as a linear combination of the basis elements with rational matrices as coefficients. This clarifies what happens under the trace, because the n …
- 12.6k
2
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Is there a field which is the union of finitely many proper subfields?
The reason it fails in the case of finite fields is the primitive element theorem (over the prime subfield, even). This is not quite an argument in the general case because of possible inseparability. …
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13
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Gossip about Grothendieck and distributive lattices
It's a tendentious question, certainly. It might mean, if Bourbaki, let us say, had had more of an interest in lattice theory, that the French word for "lattice" of this kind would be more familiar at …
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Lattice of subcategories: subobject classifier in Cat
Special cases being the submonoids of a monoid, and suborders of a partial order. What would one expect to be a common generalisation of those two, that was of interest? All one really asks for is a c …
- 12.6k
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Product lattice
Look at http://en.wikipedia.org/wiki/Lattice_%28order%29#Examples under the example it calls the Cartesian square of the natural numbers. This tells you enough about what the order will be, and the me …
- 12.6k
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Cyclic order relation in Zn
There is some sort of theory for rational linear forms in fractional parts holding at all integer multiples prime to some denominator, by Dvornicich and Zannier: see Fractional parts of linear polynom …
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