Lot R bxunitycommutative ring with(1) Prove that if a ER, then a R={arIVER}а1)anideal of R(b) is aR a maximal ideal.a

Let be a commutative ring with unity.(a) Prove that if , then is an ideal of .(b) Is a maximal…

Answered: Lot R by unity. a commutative ring with…

Lot R by unity. a commutative ring with (01) Prove that if gER, then a R={arIVER} 1) an ає idral of R₁ (6) is aR a maximal ideal. 85

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Lot R bx
unity
commutative ring with
(1) Prove that if a ER, then a R={arIVER}
а
1)
an
ideal of R
(b) is aR a maximal ideal.
a

Expert Solution

Step 1: Question Description

Let $R$ be a commutative ring with unity.

(a) Prove that if $a element of R$ , then $a R equals open curly brackets a r space vertical line space r element of R close curly brackets$ is an ideal of $R$ .

(b) Is $a R$ a maximal ideal ?

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