Hello I am just trying to work out some problems from herstein. Can you please tell me if this one is right.

If D is an integral domian and if na=0 for some a not 0 in D and for some integer n not 0 , prove that D is of finite characterstic.

so we have for some a not 0, na = 0

if b not 0 is another element in D then nab = 0b (ie) (na)b = 0

na is an element of D, an integral domain which has zero divisors, so(na)b=0 where na = 0 is justified.

However nab=0 => (nb)a=0

Here nb is an element of D and a is nonzero,

So nb = 0.

Hence the proof.

Am i right?

If D is an integral domian and if na=0 for some a not 0 in D and for some integer n not 0 , prove that D is of finite characterstic.

so we have for some a not 0, na = 0

if b not 0 is another element in D then nab = 0b (ie) (na)b = 0

na is an element of D, an integral domain which has zero divisors, so(na)b=0 where na = 0 is justified.

However nab=0 => (nb)a=0

Here nb is an element of D and a is nonzero,

So nb = 0.

Hence the proof.

Am i right?

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