Question: subject: abstract algebra Please show all work and justify each step! (a) Let R be a ring and I g R an ideal. Assume that

subject: abstract algebra

Please show all work and justify each step!

(a) Let R be a ring and I g R an ideal. Assume that R is not commutative. Prove that then R/ I is commutative if and only if ab ba 6 I for every (1, b E R. (b) Let R be a commutative ring With identity and M g R an ideal. Prove that M is the only maximal ideal of R if and only if R\\M is the set of all units in R

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