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Xy pxyxy xy R comm xpy , as required (5) (Gallian Chapter 16 # 12) If the rings R and S are isomorphic, show that R x and S x are isomorphic Solution Let ϕ R S be a ring isomorphism Define ψ R x S x by ψ anx n a 0 ϕ an x n ϕ a 0 We will prove that this is a ring isomorphism Onetoone Suppose p x ,qx R x and ψ p x ψ q xThatisE G ꂽ ̂ A M ̂ n b N ̏ ɒu Ȃ ł B A ܓ t ꍇ ͂ ݂₩ ɐ@ Ƃ Ă B ܂ A ɔG ꂽ ꍇ ́A C 悭 @ Ď R Ă BJob ID CovidGIG7cpj961 CareerBuilder TIP For your privacy and protection, when applying to a job online, never give your social security number to a prospective employer, provide credit card or bank account information, or perform any sort of monetary transaction Learn more By applying to a job using CareerBuilder you are agreeing to comply with and be subject to the CareerBuilder Terms Eƒ Ae A A ˆa E Sa A A Ae A C Aœ E œas Ae E Az A A A Ae C ƒRƒXƒ‚ƒX ‰öb ƒ\ƒtƒr
