We observe that for each $$n\ge 2$$ , the identities of stylic monoid with n generators coincide n-generated monoids from other distinguished series $$\mathscr {J}$$ -trivial studied in literature, e.g., Catalan and Kiselman monoids. This solves Finite Basis Problem

We sketch a theory of divisibility and factorization in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely topologized topological monoids. We define the topological factorization monoid, a generalization of the factorization monoid for algebraic monoids, and show that it is always topologically...