2024-03-29T12:19:21Z
https://kitami-it.repo.nii.ac.jp/oai
oai:kitami-it.repo.nii.ac.jp:00006340
2022-12-13T02:19:41Z
7:15:27
Semi-ordered Vector Space のPositive Cone になるようなSemi-ordered Space について
Some notes on semi-ordered sets which form positive Cones of semi-ordered vector spaces
磯部, 煕郎
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Let R be a semi-ordered vector space. We put R^+={x:x∈R,x≧0} R^+ is a semi-ordered set with the least element 0 and satisfies the following conditions: I.(1)for every a,b∈R^+ we have a+b∈R^+, (2)(a+b)+c=a+(b+c), (3)a+b=b+a, (4)a+0=a, (5)for every a,b∈R^+ we have a≦a+b, (6)a+c=b+c implies a=b, (7)if a≦b,then we have uniquely determined c∈R^+ such that a+c=b, II.(1)for any real number α≧O and a∈R^+ we haveαa∈R^+, (2)α(βa)=(αβ)a, (3)α(a+b)=αa+αb, (4)(α+β)a=αa+βa, (5)1a=a, Generally let x be a semi-ordered set and we assume that x satisfies the previous conditions l. (1)-(7)and II.(1)-(5). In this paper,such a semi-ordered set x is styled as “a semi-ordered set with the least element and non-negative real domain of operators". In this paper we discuss the existence of a semi-ordered vector space R which R^+=X and some properties of x.
北見工業大学
1973-10
jpn
departmental bulletin paper
https://kitami-it.repo.nii.ac.jp/records/6340
北見工業大学研究報告
5
1
103
107
https://kitami-it.repo.nii.ac.jp/record/6340/files/5-1-10.pdf
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1.6 MB
2016-11-22