The semidirectly closed pseudovariety generated by aperiodic Brandt semigroups
This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup $B_2$, denoted $\mathbf V^*(B_2)$. We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by $B_2$ which leads to the main result, which states...
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| Format: | article |
| Language: | eng |
| Published: |
2001
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| Online Access: | https://hdl.handle.net/1822/2146 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/2146 |
| Summary: | This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup $B_2$, denoted $\mathbf V^*(B_2)$. We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by $B_2$ which leads to the main result, which states that $\mathbf V^*(B_2)$ is decidable. Independently, using some suggestions given by J.~Almeida in his book ``Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in $\mathbf V^*(B_2)$. |
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