Hello,
could someone,please, define what an atom in boolean algebra is and give some examples of identifying this "species" ?
An "atom" in a Boolean Algebra is an element x, so that the only y satisfying $\displaystyle y\le x$ are x itself and 0. For example, in the Boolean algebra of sets, in which $\displaystyle \le$ is "subset" and 0 is the empty set, the atoms are the "singleton" sets, having only one member, so that the only subsets are itself and the empty set.
Let B be a set of integers (divisors of number x) and the "meet" table would contain lowest multiples of pairs of those divisors, hence each entry is a singleton and thus an atom or else I am not getting it yet ? However there is also a question of expressing non-atomic elements in y way. Which tempts me to think that some of them must be non atoms...