Null ideals and spanning ranks of matrices,II |
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| Authors: | William C Brown |
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| Institution: | Department of Mathematics , Michigan State University , East Lansing, MI, 48824 |
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| Abstract: | Suppose R is an integral domain and A ∈ M n × n(R) \{O}. If D is a spanning rank partner of A, then precisely one of the following three relationships holds: N A = N D N A = XN D or XN A = N D. Here X is an indeterminate and N A(N D) denotes the null ideal of A(D) in RX]. There are easy examples of A and D for which N A = N D and N A = XN D. In this paper, we give an example where XN A = N D. We give sharper versions of the theorem for n ≤ 4. |
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| Keywords: | Artin algebras Preprojective modules Preinjective modules Irreducible maps Auslander-Reiten quiver |
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