Does anyone know how did the idea of maximal and prime ideal came into existence for the first time ? I want to understand their applicability in mathematics.
Asked
Active
Viewed 65 times
0
-
http://math.stackexchange.com/questions/805778/maximal-ideal-prime-ideal – Zau May 29 '16 at 12:04
-
2"First time" oh boy... – IAmNoOne May 29 '16 at 12:12
-
In $\mathbb Z$ the only prime ideals are the sets $p\mathbb Z$ of multiples of $p$ where $p$ is prime . These sets are also the only maximal ideals. They have as important property that there are not zero divisors what means that $ab=0\Rightarrow$ $a=0$ or $b=0$. For example in $6\mathbb Z$ you have $2\cdot 3=0$ which is possible because $6$ is not prime. – Piquito May 29 '16 at 13:46