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Title

AN ALTERNATIVE MATRIX PROOF FOR A THEOREM OF HERSTEIN

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Abstract

 LET R BE A RING. IF WE REPLACE THE ORIGINAL ASSOCIATIVE PRODUCT OF R WITH THEIR CANONIC LIE PRODUCT, OR [A,B]=AB−BA FOR EVERY A,B IN R, THEN R WOULD BE A LIE RING. WITH THIS NEW PRODUCT THE ADDITIVE COMMUTATOR SUBGROUP OF R OR [R,R] IS A LIE SUBRING OF R. HERSTEIN HAS SHOWN THAT IN A SIMPLE RING R WITH CHARACTERISTIC UNEQUAL TO 2, ANY LIE IDEAL OF R EITHER IS CONTAINED IN Z(R), THE CENTER OF R, OR CONTAINS [R,R]. HE ALSO SHOWED THAT IN THIS SITUATION THE LIE RING [R,R]/Z[R,R] IS SIMPLE. HERE WE GIVE AN ALTERNATIVE MATRIX PROOF FOR THESE RESULTS. AS WE SHOWED IT SEEMS THAT THE CHARACTERISTIC CONDITION CAN BE PUT ON A SMALLER SET OF SIMPLE RINGS.

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    APA: Copy

    ARIANNEZHAD, M., & EMAMI, M.. (2009). AN ALTERNATIVE MATRIX PROOF FOR A THEOREM OF HERSTEIN. IRANIAN ALGEBRA SEMINAR. SID. https://sid.ir/paper/904410/en

    Vancouver: Copy

    ARIANNEZHAD M., EMAMI M.. AN ALTERNATIVE MATRIX PROOF FOR A THEOREM OF HERSTEIN. 2009. Available from: https://sid.ir/paper/904410/en

    IEEE: Copy

    M. ARIANNEZHAD, and M. EMAMI, “AN ALTERNATIVE MATRIX PROOF FOR A THEOREM OF HERSTEIN,” presented at the IRANIAN ALGEBRA SEMINAR. 2009, [Online]. Available: https://sid.ir/paper/904410/en

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