jaj•a•person's notes

Tag: m/thm/ring

See Ring theory MOC.

30 items with this tag.

A Dedekind domain admits UFI
A Dedekind domain is a CDR
A Dedekind domain is a UFD iff its ideal class group is trivial
A Dedekind domain with finitely many prime ideals is a UFD
A field contains modular arithmetic or the rationals
A finite integral domain is a field
A ring contains the integers or modular arithmetic
All primes are irreducible in an integral domain
Cayley's theorem for rings
Chinese remainder theorem for rings
Condition for a quotient commutative ring to be a field
Condition for a quotient commutative ring to be an integral domain
Cyclotomic integers
Freshman's dream
Galois field
Group of roots of unity
Hilbert's basis theorem
Ideals of a Dedekind domain need at most two generators
Integers
Lower bound on the dimension of the field of rational functions
Polynomial ring over a UFD is a UFD
Prime ideals are invertible in a Dedekind domain
Quadratic integers
Ring isomorphism theorems
Ring of integers of a number field
Subrng
The characteristic of an integral domain is 0 or prime
The polynomial ring over a field is a Euclidean domain
The polynomial ring over an integral domain is an integral domain
The ring of integers of a number field forms a lattice

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