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Some Maximal Commutative Subrings of<i>M</i><sub><i>n</i></sub>(<i>D</i>)

Some Maximal Commutative Subrings of<i>M</i><sub><i>n</i></sub>(<i>D</i>)

Abstract We answer a question of Weibel and show that maximal commutative subgrings of Artinian semisimple rings are direct products of local rings. Key Words: Maximal commutative subringsNilpotent elementsProduct of local ringsSimple Artinian rings2000 Mathematics Subject Classification: Primary 13E10Secondary 19A49 ACKNOWLEDGEMENT The author was partially supported by NSF grant DMS …