Question

Let R be a commutative ring with unity. Let I and J be ideals of R. Let D = \{x \in R \mid xb \in I \text{ for all } b \in J\}. Prove that D is an ideal of R.

Name: Let R be a commutative ring with unity. Let I and J be ideals of R. Let D = {x ∈R |xb ∈I for all b ∈J}. Prove that D is an ideal of R.
Uploaded: 2023-02-27T12:39:43-08:00
Duration: 1 min 14 s
Channel: Sri K
Description: Let R be a commutative ring with unity. Let I and J be ideals of R. Let D = {x ∈R |xb ∈I for all b ∈J}. Prove that D is an ideal of R.

          Let R be a commutative ring with unity. Let I and J be ideals of R. Let D = \{x \in R \mid xb \in I \text{ for all } b \in J\}. Prove that D is an ideal of R.

Added by Yolanda Q.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/27/2023

Step 1

Since I and J are ideals of R, they contain the zero element of R. Therefore, for any b in J, we have 0*b = 0, which means that 0 is in D. Thus, D is non-empty. Show more…

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Let R be a commutative ring with unity. Let I and J be ideals of R. Let for all binJ. Prove that D is an ideal of R. Let R be a commutative ring with unity. Let I and J be ideals of R. Let D ={x E Rxb e Ifor all b EJ}. Prove that D is an ideal of R.