How can 0=1 in a ring?!

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How can 0=1 in a ring?!

April 26, 2017ring

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How can 0=1 in a ring?!

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score 0 · Answer 1 · 2009-05-01T00:43:19+00:00

On 19 Apr, 04:29, quasi wrote: On Fri, 18 Apr 2008 19:57:11 -0700 (PDT), grocery_stocker Can someone give me a concrete example of a ring where 0=1. Thanks in advance. The zero ring. R = {0} with the obvious addition and multiplication tables. Note also that this is the only such ring, since if 0 = 1 in R then for any x in R we have x = x*1 = x*0 = 0. The zero ring plays the same role for rings, for those texts that allow it (most don’t), as the empty set does for sets. Namely it is an initial object, i.e. there is exactly one homomorphism from {0} to any ring. It’s also a terminal object, i.e. there is exactly one homomorphism from any ring to {0}. .

How can 0=1 in a ring?!

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