Z adjoin x

[wildrabbitt]

Hi,

I'd be extremely grateful if someone could explain to me what is meant by the

Z adjoin x set. Don't get me wrong, I understand what Z adjoin (root(3)) is.

I won't go into why I'm confused at the moment as I'm hoping to get a reply I can ask questions about :

http://www.mersenneforum.org/attachm...1&d=1433599291

sincerely,
William

[R.D. Silverman]

Originally Posted by wildrabbitt

Hi,

I'd be extremely grateful if someone could explain to me what is meant by the

Z adjoin x set. Don't get me wrong, I understand what Z adjoin (root(3)) is.

I won't go into why I'm confused at the moment as I'm hoping to get a reply I can ask questions about :

http://www.mersenneforum.org/attachm...1&d=1433599291

sincerely,
William

Z[x] is the set of polynomials with coefficients over Z.

[wildrabbitt]

Thanks ever so much Silverman.

My exam went well. Good to be back.

I'll have to get to grips with 'misplaced modifiers' some time soon.

[wildrabbitt]

Hi again,

I need to know what Z[I][x] means now. Could you tell me that too ? ;)


Very grateful for your previous help btw.

[xilman]

Originally Posted by wildrabbitt

Hi again,

I need to know what Z[I][x] means now. Could you tell me that too ? ;)


Very grateful for your previous help btw.

http://mathworld.wolfram.com/RingofIntegers.html

Read the whole page ...

[wildrabbitt]

Thanks. Very interesting.

I've read the whole page.

I understand what Z[ x ] is and what Z [ i ] is but not what Z[ i ][ x ] is.

[wblipp]

Originally Posted by wildrabbitt

Thanks. Very interesting.

I've read the whole page.

I understand what Z[ x ] is and what Z [ i ] is but not what Z[ i ][ x ] is.

Z[ i ] means Gaussian Integers

K [ x ] means polynomials with coefficients in K

so Z[ i ][ x ] means polynomials with Gaussian integers as coefficients

[wildrabbitt]

Beautiful. Thanks very much for that explanation.

[Nick]

The classic gentle introduction to such concepts was the book "Rings, Modules and Linear Algebra" by Brian Hartley and Trevor Hawkes. It's now out of print, but copies are still available from various sources online (or in your local university library).

Other options include the big book "Advanced Modern Algebra" by Joseph Rotman, or "Undergraduate Algebra" by Serge Lang.

[R.D. Silverman]

Originally Posted by Nick

The classic gentle introduction to such concepts was the book "Rings, Modules and Linear Algebra" by Brian Hartley and Trevor Hawkes. It's now out of print, but copies are still available from various sources online (or in your local university library).

Other options include the big book "Advanced Modern Algebra" by Joseph Rotman, or "Undergraduate Algebra" by Serge Lang.

My recommendation: Avoid Lang's books. They make good references, but lousy texts.