Finite Complete Rewriting Systems and Finite Derivation Type for Small Extensions of Monoids
نویسندگان
چکیده
منابع مشابه
Finite Complete Rewriting Systems and Finite Derivation Type for Small Extensions of Monoids
Let S be a monoid and let T be a submonoid of nite index in S. The main results in this paper state that S can be presented by a nite complete rewriting system if T can, and S has nite derivation type if T has.
متن کاملOn finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of t...
متن کاملCrystal bases , finite complete rewriting systems , and
This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...
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This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...
متن کاملHomological Finite Derivation Type
In 1987 Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness c...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7388