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About: Kasch ring     Goto   Sponge   NotDistinct   Permalink

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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. 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 . Kasch originally called Artinian rings whose proper ideals have nonzero annihilators S-rings. The characterizations below show that Kasch rings generalize S-rings.