In: Mathematica Slovaca, vol. 61, no. 3
László Fuchs
Detaily:
Rok, strany: 2011, 429 - 438
Kľúčové slová:
torsion-free, abelian groups, rank one groups, totally ordered abelian group (\mbox{{\it o-}group}), lexicographic order, archimedean order, {\it o-}cellular cover, cellular covering map, {\it o-}homomorphisms, {\it o-}cellular exact sequence
O článku:
Cellular covers of groups, and in particular,
those of divisible abelian groups, were studied in [FARJOUN, E.~D.---GÖBEL, R.---SEGEV, Y.:
\textit{Cellular covers of groups}, J. Pure Appl. Algebra \textbf{208}, (2007), 61--76], [CHACHÓLSKI,~W.---FARJOUN,~E.~D.---GÖBEL,~R.---SEGEV,~Y.: \textit{Cellular covers of divisible abelian groups}. In: Contemp. Math.~504, Amer. Math. Soc., Providence, RI, 2009, pp.~77--97],
and continued in [FUCHS,~L.---GÖBEL,~R.:
\textit{Cellular covers of abelian groups},
Results Math. \textbf{53}, (2009), 59--76]
for abelian groups in general. In this note we are investigating cellular covers in the category
of totally ordered abelian groups (called {\it o-}cellular covers; for definition see Section 2).
Some results are similar to those on \tf\ abelian groups (unordered), while others are completely different. For instance, though kernels of {\it o-}cellular covers can not be non-zero divisible groups (Lemma 3.1), they may contain non-zero divisible subgroups (Example 3.2); however, the divisible part can not be much larger than the reduced part (Theorem 3.4). There are {\it o-}groups, even among the additive subgroups of the rationals, whose {\it o-}cellular covers form
a proper class (Theorem 4.3).
Ako citovať:
ISO 690:
Fuchs, L. 2011. Cellular covers of totally ordered abelian groups. In Mathematica Slovaca, vol. 61, no.3, pp. 429-438. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0021-6
APA:
Fuchs, L. (2011). Cellular covers of totally ordered abelian groups. Mathematica Slovaca, 61(3), 429-438. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0021-6
O vydaní: