complete ring of quotients of reduced commutative rings
There is a characterization of complete ring of quotients of reduced commutative rings. Let be a reduced (http://planetmath.org/ReducedRing) commutative ring, then if is an overring of and if for any element there is an such that , then is said to be a rational extension of . See how similar this is with the definition of essential extension in the category of rings, obviously all rational extensions of reduced commutative rings are also essential extensions. Furthermore there is a maximum (upto -isomorphism) rational extension of and this is in fact the complete ring of quotients of .
|Title||complete ring of quotients of reduced commutative rings|
|Date of creation||2013-03-22 18:27:33|
|Last modified on||2013-03-22 18:27:33|
|Last modified by||jocaps (12118)|