Density of type-dependent sets in Krull monoids with analytic structure
Autor: | Maciej Radziejewski |
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Rok vydání: | 2021 |
Předmět: | |
Zdroj: | Semigroup Forum. 104:415-447 |
ISSN: | 1432-2137 0037-1912 |
DOI: | 10.1007/s00233-021-10247-1 |
Popis: | We describe structural and quantitative properties of type-dependent sets in monoids with suitable analytic structure, including simple analytic monoids, introduced by Kaczorowski (Semigroup Forum 94:532–555, 2017. 10.1007/s00233-016-9778-9), and formations, as defined by Geroldinger and Halter-Koch (Non-unique factorizations, Chapman and Hall, Boca Raton, 2006. 10.1201/9781420003208). We propose the notions of rank and degree to measure the size of a type-dependent set in structural terms. We also consider various notions of regularity of type-dependent sets, related to the analytic properties of their zeta functions, and obtain results on the counting functions of these sets. |
Databáze: | OpenAIRE |
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