A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier)
نویسندگان
چکیده
منابع مشابه
A New Niteness Condition for Monoids Presented by Complete Rewriting Systems (after Craig C. Squier)
In an unpublished preprint, Craig Squier introduces the notion of nite derivation type to show that some nitely presentable monoid has no presentation by means of a nite complete rewriting system. A similar result was already obtained by the same author using homology, but the new method is more direct and more powerful. Here, we present Squier's argument with a bit of categorical machinery, ma...
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Recently, Craig Squier introduced the notion of finite derivation type to show that some finitely presentable monoid has no presentation by means of a finite complete rewriting system. A similar result was already obtained by the same author using homology, but the new method is more direct and more powerful. Here, we present Squier’s argument with a bit of categorical machinery, making proofs ...
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Recently, Craig Squier introduced the notion of nite derivation type to show that some nitely presentable monoid has no presentation by means of a nite complete rewriting system. A similar result was already obtained by the same author using homology, but the new method is more direct and more powerful. Here, we present Squier's argument with a bit of categorical machinery, making proofs shorte...
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The geometry of the Cayley graphs of monoids defined by regular confluent monadic rewriting systems is studied. Using geometric and combinatorial arguments, these Cayley graphs are proved to be hyperbolic, and the monoids to be word-hyperbolic in the Duncan–Gilman sense. The hyperbolic boundary of the Cayley graph is described in the case of finite confluent monadic rewriting systems.
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In 1987, Craig Squier proved that, if a monoid can be presented by a finite convergent string rewriting system, then it satisfies the homological finiteness condition left-FP3. Using this result, he has constructed finitely presented decidable monoids that cannot be presented by finite convergent rewriting systems. In 1994, Squier introduced the condition of finite derivation type, which is a h...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1995
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)00043-i