Let be a commutative ring . If isn't a prime subring of then prove that has positive characteristic and therefore the ring can be written as a product where is a prime integer for .
Let be a ring . If isn't a prime subring of then prove that has positive characteristic and therefore the ring can be written as a product where is a prime integer for .
for the first part define the map by then is not injective, since is not a subring of thus , i.e. there exists some such that
the second part doesn't look correct to me! are you sure shouldn't be a "prime power" instead of "prime"?
for the first part define the map by then is not injective, since is not a subring of thus , i.e. there exists some such that
the second part doesn't look correct to me! are you sure shouldn't be a "prime power" instead of "prime"?
Thank you very much for the first part , about the second part ; there is written prime integer in the statement but how can you solve it if it was "prime power" instead ?
Thank you very much for the first part , about the second part ; there is written prime integer in the statement but how can you solve it if it was "prime power" instead ?
well, let and consider the prime factorization of n: let see that for and
thus, by the Chinese remainder theorem for rings, we have finally put and see that