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Quick ring questionby 1MileCrash
Tags: ring 
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#1
Mar3114, 04:42 PM

P: 1,305

Is (x) * y = x * (y) true for all rings?
It seems simple enough but I feel like * must be commutative when trying to prove this. 


#2
Mar3114, 04:50 PM

P: 1,305

Never mind, I have it.
But how can I show that 1 * 1 = 1 where 1 is the multiplicative identity? 


#3
Mar3114, 07:27 PM

HW Helper
P: 2,264

Use the distributive property with
(1)(1+(1))=0 


#4
Mar3114, 08:29 PM

P: 1,305

Quick ring question
(1)(1) + (1)(1) = 0 1 + (1)(1) = 0 (1)(1) = 1 by definition 


#5
Mar3114, 08:49 PM

Mentor
P: 21,408

1 + (1) = 0 since 1 and 1 are additive inverses of each other 1(1 + (1)) = 1(0) = 0, since 0 times anything is 0. 1(1) + (1)(1) = 0 Since 1(1) and (1)(1) add to zero, they are additive inverses. We know that 1(1) = 1, since 1 is the multiplicative identity, so 1(1) must equal 1. 


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