a,b in field. ab = 0. show a = 0 or b = 0 (1 Viewer)

[underthesun]

yeah, so that's the question. Its off my finite maths textbook,

let F be a field and a, b in F with ab = 0. Show that a = 0 or b = 0.

Is it because, in a field, a x b will never equal zero, unless a = 0 or b = 0? But then that's the given statement.. aarrrrghhhhh!

 

[McLake]

This is one of those silly "introduction" questions.

I think you are meant to answer it something like this:

Two cases:
Let a != 0. ab = 0, so b = 0.
Let a = 0.

So either a or b = 0.

 

[Euler]

we are working in a field, so if a is not zero, then it has an inverse, call it c.

then ac = ca = 1

since ab = 0, then 0 = c.0 = c.ab = b

so b = 0.

 

[turtle_2468]

Ahh this brings back fond memories...

 

[underthesun]

ugh.. i have a feeling that finite will be very ugly...
thanks a lot dudes!

btw turtle, you must be the guy who does med while doing lots of maths ey

 

[turtle_2468]

yeah... well I don't do that much volume but it's good stuff
BTW apparently finite is a relative walk in the park compared to discrete..

 

[McLake]

yeah... well I don't do that much volume but it's good stuff
BTW apparently finite is a relative walk in the park compared to discrete..

Um, NO! Finite is far harder (trust me).

 

[underthesun]

if "relative walk in the park" comes from someone other than turtle, then maybe its true, but if its from the undisputed king of maths.. (doesnt hold much ground now does it? )

 

[turtle_2468]

Although, I reckon mclake has _actually_ done finite whereas I haven't... hence the "apparently"...
but algebra is fun Well I have an assignment due now so maybe I should actually stop wasting time..

 

[McLake]

Although, I reckon mclake has _actually_ done finite whereas I haven't... hence the "apparently"...

Yes, I have.

 

[BlackJack]

Um, NO! Finite is far harder (trust me).

Now THAT brings back fond memories...

Not that I'm qualified to say, but I support finite being harder.

 

[xiao1985]

Although, I reckon mclake has _actually_ done finite whereas I haven't... hence the "apparently"...
but algebra is fun Well I have an assignment due now so maybe I should actually stop wasting time..

...

i wanna change myname to turtle wannabe???
really, i mean, i dreamt of becoming a maths person...

 

[McLake]

Now THAT brings back fond memories...

*Tries to rekindle same memories and fails*

*Says hi to BJ instead*