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These bundles include a select Ring device of the customer’s choosing, as well as a lifetime Ring Protect Basic subscription (for the useful lifetime of the device), and a 3-year limited warranty on the device.Jul 31, 2017 · Let R be a commutative ring with 1. Prove that the principal ideal ( x) generated by the element x in the polynomial ring R [ x] is a prime ideal if and only if R is an integral domain. Prove also that the ideal ( x) is a maximal ideal if and only if R is a field. Add to solve later Sponsored Links Contents [ hide] Problem 198 Proof. Hence P ( X) under symmetric difference and intersection is a commutative ring with the unity. Obviously it is not true that for any set A ∈ P ( X), there is a set B ∈ P ( X) that A ∩ B = X. Thus P ( X) under symmetric difference and intersection is not a field. 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