Mathieu Subspace

A Mathieu subspace of an associative algebra over a field , where has an identity element, is a subspace of over such that if for every , then for every fixed pair and all sufficiently large (Zhao 2012). In a commutative algebra, this reduces to requiring that for every imply for every fixed and all sufficiently large . Every ideal of is a Mathieu subspace, so Mathieu subspaces generalize ideals. They occur in the formulation of the image conjecture.