The product of divisibility groups (G1,O1)×(G2,O2) with G1 finitely generated

Autor:	Yves Lequain
Rok vydání:	2008
Předmět:	Discrete mathematics Algebra and Number Theory Group (mathematics) Product (mathematics) Torsion (algebra) Finitely-generated abelian group Divisibility rule Lattice (discrete subgroup) Mathematics
Zdroj:	Journal of Algebra. 319:2979-2993
ISSN:	0021-8693
Popis:	We show that: (1) If ( G 1 , O 1 ) is a finitely generated divisibility group that is not lattice ordered and if ( G 2 , O 2 ) is a divisibility group such that Card ( G 2 ) > Card ( R ) , then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is not a divisibility group. (2) If ( G 1 , O 1 ) is a torsion free finitely generated divisibility group and if ( G 2 , O 2 ) is a lattice ordered group with only finitely many ultra filters, then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is a divisibility group if and only if Card ( G 2 ) ⩽ Card ( R ) . (3) If ( G 1 , O 1 ) and ( G 2 , O 2 ) are both torsion free finitely generated divisibility groups, then the product ( G 1 , O 1 ) × ( G 2 , O 2 ) is a divisibility group.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4e79b70801bf50ecff3482aa49f15e15 https://doi.org/10.1016/j.jalgebra.2007.07.020 Zobrazit plný text záznamu Full Text from ScienceDirect