Link between a natural centralizer and the smallest essential ideal in structural matrix rings |
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| Authors: | Leon Van wyk |
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| Institution: | Department of Mathematics , University of Stellenbosch , Private Bag XI, Stellenbosch, 7602, South Africa E-mail: lvw@land. sun. ac.za |
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| Abstract: | In a structural matrix ring Mn (ρ R) over an arbitrary ring R we determine the centralizer of the set of matrix units in Mn (ρR) associated with the anti-symmetric part of the reflexive and transitive binary relation ρ on {1,2,…,n}. If the underlying ring R has no proper essential ideal, for example if R is a field, then we show that the largest ideal of Mn (ρR) contained in the mentioned centralizer coincides with the smallest essential ideal of Mn (ρR). |
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| Keywords: | Structural matrix ring centralizer esential ideal |
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