A trouble concerning excellent

Let R be a commutative ring and also I and also J be 2 perfects of R, just how to show that IJ = the junction of I and also J if R = I+J?

2019-12-02 03:10:52
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Answers: 1

HINT $\ $ One instructions is unimportant. The various other instructions calls for more theories, as an example if $\rm\ I + J = 1\ $ after that begin with the reality that $\rm\ (I+J)\ \ (I\cap J) \ \subseteq\ I\:J\ $ adheres to by using the distributive regulation. It is an excellent kind of the integer regulation $\rm gcd(i,j)\ lcm(i,j) = i\:j\ \ $ so $\rm\ \ gcd(i,j)=1\ \Rightarrow\ lcm(i,j) = i\:j\:.$

2019-12-03 05:08:58