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Define this please (possibly polynomial rings)

What does this mean:

R[x]1 R[x]_{1}

or is it:

R[x]1 \mathbb{R}[x]_{1}

I think it is something to do with polynomial rings.

Cheers
Reply 1
Avatar for Dragon
Dragon
10
R[x] R[x] is the polynomial ring (of one variable) over the ring R. So R[x] \mathbb{R}[x] would be the polynomial ring over the real numbers, which is also a ring.

As for the subscript 1, I've never seen that before in this context. Where did you get it from?
Reply 2
Avatar for adie_raz
adie_raz
OP
1
Original post by Dragon
R[x] R[x] is the polynomial ring (of one variable) over the ring R. So R[x] \mathbb{R}[x] would be the polynomial ring over the real numbers, which is also a ring.

As for the subscript 1, I've never seen that before in this context. Where did you get it from?


I got it from some scribbles I made in my lectures, otherwise it would have been easy to figure out what it was as it would have been defined by my lecturer. I am not sure, I thought maybe it was the order of the polynomial...
Reply 3
Avatar for Dragon
Dragon
10
I'm sure your lecturer would have noted the significance of the subscript if he wrote it there. Aren't there any online lecture notes?
Reply 4
Avatar for SsEe
SsEe
13
Original post by adie_raz
I got it from some scribbles I made in my lectures, otherwise it would have been easy to figure out what it was as it would have been defined by my lecturer. I am not sure, I thought maybe it was the order of the polynomial...


It might have been R[x1]R[x_1]. You can have polynomial rings in several variables which you could write as R[x1,x2,...,xn]R[x_1, x_2, ..., x_n]
Reply 5
Avatar for adie_raz
adie_raz
OP
1
I have found it about five pages on:

R[x]1={a+bx;a,bϵR} \mathbb{R}[x]_{1} = \{a+bx; a, b \epsilon \mathbb{R} \} is NOT a ring: multiplication is NOT closed.


That is all I can find on it... Thank you for defining the difference between R[x] R[x] and R[x] \mathbb{R}[x] though :biggrin:
(edited 13 years ago)
Reply 6
Avatar for Dragon
Dragon
10
So all polynomials of degree 1 or less.
Reply 7
Avatar for adie_raz
adie_raz
OP
1
Original post by Dragon
So all polynomials of degree 1 or less.


Yes I would say so, that is literally the only line I have.

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