EXTERIOR DEPTH AND EXTERIOR GENERIC ANNIHILATOR NUMBERS
Autor(en): | Kaempf, Gesa Kubitzke, Martina |
Stichwörter: | ALEXANDER DUALITY; Annihilator numbers; Betti numbers; Depth; Exterior algebra; Mathematics; RESOLUTIONS | Erscheinungsdatum: | 2012 | Herausgeber: | TAYLOR & FRANCIS INC | Journal: | COMMUNICATIONS IN ALGEBRA | Volumen: | 40 | Ausgabe: | 1 | Startseite: | 1 | Seitenende: | 25 | Zusammenfassung: | We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module, we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior algebraic shifting. We define exterior annihilator numbers analogously to the annihilator numbers over the polynomial ring introduced by Trung [19] and Conca et al. [9]. In addition to a combinatorial interpretation of the annihilator numbers, we show how they are related to the symmetric Betti numbers and the Cartan-Betti numbers, respectively. We finally conclude with an example which shows that neither the symmetric nor the exterior generic annihilator numbers are minimal among the annihilator numbers with respect to a sequence. |
ISSN: | 00927872 | DOI: | 10.1080/00927870903386486 |
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geprüft am 17.05.2024