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  1. 紀要掲載論文
  2. 北見工業大学研究報告
  3. Vol.5

Semi-ordered Vector Space のPositive Cone になるようなSemi-ordered Space について

https://kitami-it.repo.nii.ac.jp/records/6340
https://kitami-it.repo.nii.ac.jp/records/6340
a62ce050-0b68-4853-aac5-e2263b171938
名前 / ファイル ライセンス アクション
5-1-10.pdf 5-1-10.pdf (1.6 MB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2007-04-09
タイトル
タイトル Semi-ordered Vector Space のPositive Cone になるようなSemi-ordered Space について
言語
言語 jpn
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
その他のタイトル
その他のタイトル Some notes on semi-ordered sets which form positive Cones of semi-ordered vector spaces
著者 磯部, 煕郎

× 磯部, 煕郎

WEKO 32233

磯部, 煕郎

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著者別名
識別子 32234
識別子Scheme WEKO
姓名 ISOBE, Kiro
抄録
内容記述タイプ Abstract
内容記述 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.
書誌情報 北見工業大学研究報告

巻 5, 号 1, p. 103-107, 発行日 1973-10
フォーマット
内容記述タイプ Other
内容記述 application/pdf
著者版フラグ
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出版者 北見工業大学
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