Please help with proof:: Let R be a commutative ring and let q be a fixed element in R. Prove that the set Q = { such that r = t*q for some element } is an ideal of R.

Question

Please help with proof::  Let R be a commutative ring and let q be a fixed element in R. Prove that the set Q = {  such that r = t*q for some element  } is an ideal of R.

amistre64 · Answer

might help to define properties of a commutative ring,  and also the properties of an ideal to be able to have some sort of a guide towards the proof

anonymous · Answer

so question.  do i prove it's nonempty, closed under subtraction, and closed under multiplication?

amistre64 · Answer

you hypothesis implies the properties of the ring so you do not need to prove that its a ring,

if memory serves, an ideal is a subring, or possible a subset of elements, that are closed within the ideal itself

anonymous · Answer

thank you. i will give it a go