Let R be a ring. (a) Show that R has exactly one zero, 0R. (b) If R also has an identity, 1R, show that 1R is the only identity. (c) Can a unit in R have more than one inverse? If yes, give an example. If no, prove it.

Let R be a ring. (a) Show that R has exactly one zero, 0R. (b) If R also has an identity, 1R, show that 1R is the only identity. (c) Can a unit in R have more than one inverse? If yes, give an example. If no, prove it.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Let R be a ring.
(a) Show that R has exactly one zero, 0_R.
(b) If R also has an identity, 1_R, show that 1_R is the only identity.
(c) Can a unit in R have more than one inverse? If yes, give an example. If no, prove it.

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