Factoriality in Riesz groups
Throughout let G = (G,+,≤, 0) denote a Riesz group, where + is not necessarily a commutative operation. Call x ∈ G homogeneous if x > 0 and for all h, k ∈ (0, x] there is t ∈ (0, x] such that t ≤ h, k. In this paper we develop a theory of factoriality in Riesz groups based on the fact that if x ≤...
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| Veröffentlicht in: | Journal of group theory 2008-01, Vol.11 (1), p.23-41 |
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| container_title | Journal of group theory |
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| creator | Mott, Joe L Rashid, Muneer A Zafrullah, Muhammad |
| description | Throughout let G = (G,+,≤, 0) denote a Riesz group, where + is not necessarily a commutative operation. Call x ∈ G homogeneous if x > 0 and for all h, k ∈ (0, x] there is t ∈ (0, x] such that t ≤ h, k. In this paper we develop a theory of factoriality in Riesz groups based on the fact that if x ≤ G and x is a finite sum of homogeneous elements then x is uniquely expressible as a sum of finitely many mutually disjoint homogeneous elements. We then compare our work with existing results in lattice-ordered groups and in (commutative) integral domains. |
| doi_str_mv | 10.1515/JGT.2008.002 |
| format | Article |
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| source | De Gruyter journals |
| title | Factoriality in Riesz groups |
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