Aufsatz in einer Fachzeitschrift
For finitely presented monoids the homological finiteness conditions FHT and bi-FP3 coincide
Details zur Publikation
Autor(inn)en: | Kobayashi, Y.; Otto, F. |
Publikationsjahr: | 2003 |
Zeitschrift: | Journal of Algebra |
Seitenbereich: | 327-341 |
Jahrgang/Band : | 264 |
Erste Seite: | 327 |
Letzte Seite: | 341 |
ISSN: | 0021-8693 |
eISSN: | 1090-266X |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, Abstract
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 FP3, but for finitely presented monoids in general it is strictly stronger than the conditions left-FP3 and right-FP3 together. Here we define the notion of bi-FPn 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-FP3. (C) 2003 Elsevier Science (USA). All rights reserved.
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 FP3, but for finitely presented monoids in general it is strictly stronger than the conditions left-FP3 and right-FP3 together. Here we define the notion of bi-FPn 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-FP3. (C) 2003 Elsevier Science (USA). All rights reserved.
