Linear L-Algebras and Prime Factorization

A complete recursive description of noetherian linear KL-algebras is given. L-algebras form a quantum structure that occurs in algebraic logic, combinatorial group theory, measure theory, geometry, and in connection with solutions to the Yang-Baxter equation. It is proved that the self-similar closure of a noetherian linear KL-algebra is determined by its partially ordered set of primes, and that its elements admit a unique factorization by a decreasing sequence of prime elements.