What is the name of a "basis" in Boolean algebras So, a basis in linear algebra is the smallest set which generates a particular vector space. (More formally, a subset of the vector space which is linearly independent and spans the vector space)
Is there a name for a similar concept in Boolean algebra? The object I am describing is a subset A of the elements of the boolean algebra such that


*

*The set A generates the boolean algebra

*No proper subset of A generates the boolean algebra.


There is no particular name for this.  I would refer to it simply as a "minimal generating set".  Note that in contrast to the case of vector spaces, minimal generating sets for the same Boolean algebra can have different cardinalities, and they will not always freely generate the algebra, so the notion is much less useful than the notion of a basis for a vector space.
(In fact, I suspect some Boolean algebras don't even have a minimal generating set, though I don't know an example.)
