Arithmetic of semigroups of series in multiplicative systems

• Date: 2009
• Main Authors: Il’inskaya, I. P., Ильинская, И. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3068
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We study the arithmetic of a semigroup $\mathcal{M}_P$ of functions with operation of multiplication representable in the form $f(x)=∑^{∞}_{n=0} a_nχ_n(x)\left(a_n≥0,\; ∑^{∞}_{n=0}a_n =1 \right)$, where $\{χ_n|\}^{∞}_{n=0}$ is a system of multiplicative functions that are generalizations of the clas...