On the solvability of equations in semigroups with $x^r=x$

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.

Basic information

• Original name: On the solvability of equations in semigroups with $x^r=x$
• Authors: KLÍMA, Ondřej.
• Edition: Klagenfurt, Proceedings of 58th Workshop on General Algebra "58. Arbeitstagung Allgemeine Algebra" p. 237-246, Contributions to General Algebra 12, 2000.
• Publisher: Verlag Johannes Heyn

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10101 Pure mathematics
• Country of publisher: Austria
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14310/00:00002351
• Organization unit: Faculty of Science
• ISBN: 3-85366-951-4

Abstract

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.

Links

• MSM 143100009, plan (intention): Name: Matematické struktury algebry a geometrie

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry