On the solvability of equations in semigroups with $x^r=x$
| Authors | |
|---|---|
| Year of publication | 2000 |
| Type | Article in Proceedings |
| Conference | Proceedings of 58th Workshop on General Algebra "58. Arbeitstagung Allgemeine Algebra" |
| MU Faculty or unit | |
| Citation | KLÍMA, Ondřej. On the solvability of equations in semigroups with $x^r=x$. In Proceedings of 58th Workshop on General Algebra "58. Arbeitstagung Allgemeine Algebra". Klagenfurt: Verlag Johannes Heyn, 2000, p. 237-246. Contributions to General Algebra 12. ISBN 3-85366-951-4. |
| Field | General mathematics |
| Description | The word problem for the free semigroups satisfying the identity $x^r=x$ was reduced to the word problem for the free groups satisfying the identity $x^{r-1}=1$ by Kaďourek and Polák in 1990. We use their result to solve the equations with constants in the free semigroups in the varieties $\Sr$. In fact, we transform the problem of solvability of a single equation in $\Sr$ into the problem of solvability of disjunction of equations with constants in $\Gr$. This is shown in detail for equations with two and three constants. |
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