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Factoriality in Riesz groups
被引:5
|作者:
Mott, Joe L.
[1
]
Rashid, Muneer A.
[2
]
Zafrullah, Muhammad
机构:
[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA
[2] Natl Univ Sci & Technol, Ctr Adv Math & Phys, Rawalpindi, Pakistan
关键词:
D O I:
10.1515/JGT.2008.002
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
Throughout let G = (G, +, <=, 0) denote a Riesz group, where + is not necessarily a commutative operation. Call x epsilon G homogeneous if x > 0 and for all h, k epsilon (0, x] there is t epsilon (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 epsilon 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.
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页码:23 / 41
页数:19
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