Kasch_ring
In ring theory, a subfield of abstract algebra, a right Kasch ring is a ring R for which every simple right R module is isomorphic to a right ideal of R.[1] Analogously the notion of a left Kasch ring is defined, and the two properties are independent of each other.
Kasch rings are named in honor of mathematician Friedrich Kasch. Kasch originally called Artinian rings whose proper ideals have nonzero annihilators S-rings. [2][3] The characterizations below show that Kasch rings generalize S-rings.