The semigroup generated by regular Boolean matrices (Q1849319)
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scientific article; zbMATH DE number 1836972
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The semigroup generated by regular Boolean matrices |
scientific article; zbMATH DE number 1836972 |
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The semigroup generated by regular Boolean matrices (English)
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1 December 2002
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This paper deals with the semigroup \(B_n^r\) of multiplicative Boolean matrices which are products of regular Boolean matrices. An algorithm is given to determine membership of a matrix in this semigroup, it is proved that Green's relation classes of elements of \(B_n^r\) are the same as the classes of those elements in \(B_n\), and using Breen's work, that the height of the poset of \(\mathcal D\)-classes is at least the \(n+3\)-rd Fibonacci number minus 2.
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regular Boolean matrices
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Green relations
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posets of \(\mathcal D\)-classes
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semigroups of Boolean matrices
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