| Abstract:
A finite variety is a class of algebra which is closed under the
formation of homomorphic images, subalgebras, and finite direct products.
We are interested in computing the ratio of the number of directly
irreducible algebras of size \( \le n \)
to the number of all algebras of size \( \le n \).
For instance, for boolean algebras, there is one directly irreducible, of
size 2, and one algebra of size \( 2^n \) for
\( n \ge 0 \); thus, the ratio goes to 0.
For finite varieties of lattices, I will prove that the ratio goes to
1.
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