Homological Finite Derivation Type
Homological Finite Derivation Type
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同调有限导数类型
DOI：
10.1142/s0218196703001407
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
S. Hermiller
中科院分区：
文献类型：
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作者：
J. M. Alonso;S. Hermiller
1987年，Squier定义了有限导子型的概念。为了做到这一点，他将一个2-复形与演示相关联。幺半群然后有有限导子型，如果，模的作用的自由幺半群环，1维同伦的这个复杂的是numerous产生。Cremanns和Otto证明了有限导子型蕴涵着左FP 3的同调有限性条件，并且当么半群是群时，这两个性质是等价的。在本文中，我们定义了一个新的版本的有限导子类型，基于同调信息，连同这种有限导子类型的扩展到更高的维度，并显示连接到同调类型FPn的么半群和组。
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 condition left FP3, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with an extension of this finite derivation type to higher dimensions, and show connections to homological type FPn for both monoids and groups.