VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Productivity of the Zariski topology on groups
    Dikranjan, Dikran N., 1950- ; Toller, Daniele
    This paper investigates the productivity of the Zariski topology ▫$\mathfrak Z_G$▫ of a group ▫$G$▫. If ▫$\mathcal G = \{G_i\mid i\in I\}$▫ is a family of groups, and ▫$G = \prod_{i\in I}G_i$▫ is ... their direct product, we prove that ▫$\mathfrak Z_G \subseteq \prod_{i\in I}\mathfrak Z_{G_i}$▫. This inclusion can be proper in general, and we describe the doubletons ▫$\mathcal G = \{G_1,G_2\}$▫ of abelian groups, for which the converse inclusion holds as well, i.e., ▫$\mathfrak Z_G = \mathfrak Z_{G_1} \times \mathfrak Z_{G_2}$▫. If ▫$e_2 \in G_2$▫ is the identity element of a group ▫$G_2$▫, we also describe the class ▫$\Delta$▫ of groups ▫$G_2$▫ such that ▫$G_1 \times \{e_{2}\}$▫ is an elementary algebraic subset of ▫${G_1 \times G_2}$▫ for every group ▫$G_1$▫. We show among others, that ▫$\Delta$▫ is stable under taking finite products and arbitrary powers and we describe the direct products that belong to ▫$\Delta$▫. In particular, ▫$\Delta$▫ contains arbitrary direct products of free non-abelian groups.
    Vir: Commentationes Mathematicae Universitatis Carolinae. - ISSN 0010-2628 (Vol. 54, no. 2, 2013, str. 219-237)
    Vrsta gradiva - članek, sestavni del
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 16631897

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