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21. Let R be a ring and let a be a nonzero element of R that is not a zero divisor. Prove that cancelation holds for a; that is, prove that (a) If ab (b) If ba ac in R, then b = c. ca in R, then b = c.

21. Let R be a ring and let a be a nonzero element of R that is not a zero divisor. Prove that cancelation holds for a; that is, prove that (a) If ab (b) If ba ac in R, then b = c. ca in R, then b = c.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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21. Let R be a ring and let a be a nonzero element of R that is not a zero divisor. Prove that cancelation holds for a; that is, prove that (a) If ab ac in R, then b = c. = (b) If ba = ca in R, then b = c.
Transcribed Image Text:21. Let R be a ring and let a be a nonzero element of R that is not a zero divisor. Prove that cancelation holds for a; that is, prove that (a) If ab ac in R, then b = c. = (b) If ba = ca in R, then b = c.
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