On the nilpotent matrices over \(D_{01}\)-lattice (Q1595211)
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scientific article; zbMATH DE number 1563544
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nilpotent matrices over \(D_{01}\)-lattice |
scientific article; zbMATH DE number 1563544 |
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On the nilpotent matrices over \(D_{01}\)-lattice (English)
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28 October 2001
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A \(D_{01}\)-lattice \(L\) is a distributive lattice such that \(0,1\in L\) and \(0\leq x\leq 1\) \(\forall x\in L\). By defining \(a+b=a\vee b\) and \(ab=a\wedge b\), \(L\) becomes a ring. The properties of nilpotent matrices in \(M_n(L)\) are studied and a necessary and sufficient condition for a matrix \(A\in M_n(L)\) to be nilpotent is also established.
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nilpotent matrices
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fuzzy relations
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