On 2007-11-13, Jamie <jamievicary@xxxxxxxxx> wrote:
Is there a straightforward algebraic characterisation of the subrings
of the complex numbers? Any such subring must be commutative, of
characteristic 0, have 0=/=1, and be without zero divisors (so ab=0
implies a=0 or b=0). But in particular this still leaves polynomial
rings, which are not subrings of the complex numbers.
Hm, what if we take the subring Q[e], or C[e], where e is the base of
the natural log? That are polynomial rings, right?
ring theorists should be shot (happy holidays) ... was one that makes the image of a homomorphism a subring... the category of commutative unitary rings with standard morphism (i.e. ..."rational extension" is a bit more complicated!) ... and then go on to choose this route with homomorphisms not respecting ... (sci.math)
Re: homomorphism of module ... abelian group M over a ring R is to exhibit a homomorphism ... then m -> r.m is homomorphism.... I like my rings with identity. ... I wouldn't call 2Z a subring at all; precisely since I prefer my rings to ... (sci.math)
Re: Ring Theory Problem ... Are your rings also commutative? ... if we assume rings always have unity (though subrings need ... define a "unitary subring" to be a subring whose unity is the same as ... --- Calvin... (sci.math)
Re: Is every subring of Z is of the form mZ ? ...student a écrit: ... subset of Z of the form mZ is a subring of Z, but, why the opposite?... If you want rings and subrings to be unitary, Z is the only subring of Z. ... (sci.math)
Re: Prime Spectrum and Axiom of Choice ... Perhaps you missed my other reply -- I posted a counterexample.... whether all rings are actually ... condition for P implies P is isolated.. ... This then implies that for all P_0 in Spec R \ ... (sci.math)
