irreducible element

In a monoid, an element $x$ is **irreducible** if it is neither invertible nor the product of two non-invertible elements. Without bias, we can say that $x$ is irreducible if, whenever it is written as a product of a finite list of elements, at least one element in the list is invertible.

Last revised on August 29, 2018 at 14:24:04. See the history of this page for a list of all contributions to it.