For finitely presented monoids the homological finiteness conditions FHT and bi-FP3 coincide
✍ Scribed by Yuji Kobayashi; Friedrich Otto
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 149 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
FHT is a homological finiteness condition of monoids that was introduced by Pride and Wang. For finitely presented groups this property is equivalent to the homological finiteness condition FP 3 , but for finitely presented monoids in general it is strictly stronger than the conditions left-FP 3 and right-FP 3 together. Here we define the notion of bi-FP n for monoids, using bimodules instead of left-or right-modules, and by establishing an exact sequence involving the relation bimodule of a monoid, we prove that for finitely presented monoids the property FHT is equivalent to the finiteness condition bi-FP 3 .