On the inverse transversals of \(M_{F,n}\) and its core \(\langle E(M_{F,n})\rangle\). (Q1430474)
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scientific article; zbMATH DE number 2067244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the inverse transversals of \(M_{F,n}\) and its core \(\langle E(M_{F,n})\rangle\). |
scientific article; zbMATH DE number 2067244 |
Statements
On the inverse transversals of \(M_{F,n}\) and its core \(\langle E(M_{F,n})\rangle\). (English)
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27 May 2004
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A subsemigroup \(T\) of a regular semigroup \(S\) is called an inverse transversal of \(S\) if for every \(a\in S\) there exists a unique inverse of \(a\) which belongs to \(T\). It is shown that neither the multiplicative semigroup of all \(n\times n\) matrices over a field nor its core contain an inverse transversal.
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inverse transversals
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regular semigroups
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idempotents
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cores
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semigroups of matrices
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