# Free Boolean Algebra

Please help answer the following question.

Using your knowledge of free objects in a category, give a definition of a free Boolean algebra B on a set D. How these compare to free Boolean rings?

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#### Solution Preview

Problem: Using your knowledge of free objects in a category, give a definition of a free Boolean algebra B on a set D. How these compare to free Boolean rings?

Solution:

A Boolean algebra B is called free on a set D if there is a mapping f:D-->B such that for any Boolean algebra B' and a mapping f':D-->B' there exists a unique Boolean algebras homomorphism g:B-->B' such that gf=f'. In fact, the free Boolean algebra on a set D is the image of D under the left adjoint functor of the forgetful functor ...

#### Solution Summary

This posting helps with a free Boolean algebra question. It gives a definition of a free Boolean algebra B on a set D using the knowledge of free objects in a category. It discusses how these compare to free Boolean rings. Step by step calculations are provided with detailed explanations for each of the steps.