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Let R be a ring such that 0 is both the additive identity and the mu.pdf

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Let R be a ring such that 0 is both the additive identity and the multiplicative identity. Show that there is only one element in R. Solution Let a be an arbitrary element of the ring R. Since 0 is the multiplicative identity, we have 0 *a = a *0 = a. However, 0 * a = a *0 = 0 for all a in R. Therefore a = 0. Thus, there is only one element in R i.e. 0..

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Let R be a ring such that 0 is both the additive identity and the multiplicative identity. Show that there is only one element in R. Solution Let a be an arbitrary element of the ring R. Since 0 is the multiplicative identity, we have 0 *a = a *0 = a. However, 0 * a = a *0 = 0 for all a in R. Therefore a = 0. Thus, there is only one element in R i.e. 0.

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Let R be a ring such that 0 is both the additive identity and the mu.pdf

  • 1. Let R be a ring such that 0 is both the additive identity and the multiplicative identity. Show that there is only one element in R. Solution Let a be an arbitrary element of the ring R. Since 0 is the multiplicative identity, we have 0 *a = a *0 = a. However, 0 * a = a *0 = 0 for all a in R. Therefore a = 0. Thus, there is only one element in R i.e. 0.