FOM: rings vs. algebras

Kanovei kanovei at
Sun Mar 15 15:06:34 EST 1998

<Date: Sun, 15 Mar 1998 10:44:14 -0800
<From: Vaughan Pratt <pratt at>

<every Boolean ring *is* a Boolean algebra 

Let me stick on this claim. 

As it is clear that 
formally BR and BA are objects of different signature, 
the only way I see to understand the claim is that there 
is a definition of the signature of BR in terms of the 
signature of BA, and a definition in the opposite 
direction, which convert each BA in BR and vice versa, 
and (most likely) give the identity in composition 
(modulo isomorphism). 

Is there such ? Or the reasoning is driving at something 
like *clones of hemidemisemifemtomorphism* ?

Please continue to comment. 

Vladimir Kanovei 

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