Homological finite derivation type

Alonso, Juan and Hermiller, Susan M. (2003) Homological finite derivation type. International Journal of Algebra and Computation, 13 (3). pp. 341-359.

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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.

Item Type:Article
Additional Information:World Scientific Publishing Company.
ID Code:2780
Deposited On:12 Jun 2008
Last Modified:18 Nov 2009 16:14

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