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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/6340a62ce050-0b68-4853-aac5-e2263b171938
名前 / ファイル | ライセンス | アクション |
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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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 |
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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 |
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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 | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | 北見工業大学 |