Power monoids and their arithmetic: a survey

Abstract: The non-empty finite subsets of a multiplicatively written monoid form a monoid in their own right, and so do the finite subsets that contain the identity element. Partly due to their unusual arithmetic properties, these structures, known as power monoids, have attracted increasing attention in recent years and have in turn stimulated growing interest in new perspectives in factorization theory, better suited to non-cancellative settings. We survey these developments and briefly review some related aspects.