The Freiheitssatz for One-Relation Monoids
نویسندگان
چکیده
منابع مشابه
Decision Problems for Finitely Presented and One-Relation Semigroups and Monoids
For some distinguished properties of semigroups, such as having idempotents, regularity, hopficity etc, we study the following: whether that property or its negation is a Markov property, whether it is decidable for finitely presented semigroups and for one-relation semigroups and monoids. All the results and open problems are summarized in a table.
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We prove the Freiheitssatz for free associative algebras over any field. This extends the previous result of Marker-Limanov and immediately implies the Freiheitssatz for free restricted Lie algebras and free Lie algebras. We prove the Freiheitssatz for free Poisson algebras over a field of characteristic zero. This answers a question of MarkerLimanov and Umirbaev in the affirmative.
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It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
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The classical results of Magnus on one-relator groups (such as the Freiheitssatz and the solvability of the generalized word problem for Magnus subgroups) are generalized to some (nitely presented groups whose relators are constructed inductively. The diagrammatic asphericity of such group presentations is also proven. c © 2001 Elsevier Science B.V. All rights reserved. MSC: Primary 20F05; 20F0...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.2307/2045488