教師資料查詢 | 類別: 期刊論文 | 教師: 譚必信 Tam Bit-shun (瀏覽個人網頁)

標題:On the semiring of cone preserving maps
學年69
學期2
出版(發表)日期1981/02/01
作品名稱On the semiring of cone preserving maps
作品名稱(其他語言)
著者Tam, Bit-shun
單位淡江大學數學學系
出版者New York : Elsevier Inc.
著錄名稱、卷期、頁數Linear Algebra and Its Applications 35, pp.79-108
摘要If K is a proper cone in Rn, then the cone of all linear operators that preserve K, denoted by π(K), forms a semiring under usual operator addition and multiplication. Recently J.G. Horne examined the ideals of this semiring. He proved that if K1, K2 are polyhedral cones such that π(K1) and π(K2) are isomorphic as semirings, then K1 and K2 are linearly isomorphic. The study of this semiring is continued in this paper. In Sec. 3 ideals of π(K) which are also faces are characterized. In Sec. 4 it is shown that π(K) has a unique minimal two-sided ideal, namely, the dual cone of π(K∗), where K∗ is the dual cone of K. Extending Horne's result, it is also proved that the cone K is characterized by this unique minimal two-sided ideal of π(K). The set of all faces of π(K) inherits a quotient semiring structure from π(K). Properties of this face-semiring are given in Sec. 5. In particular, it is proved that this face-semiring admits no nontrivial congruence relation iff the duality operator of π(K) is injective. In Sec. 6 the maximal one-sided and two-sided ideals of π(K) are identified. In Sec. 8 it is shown that π(K) never satisfies the ascending-chain condition on principal one-sided ideals. Some partial results on the question of topological closedness of principal one-sided ideals of π(K) are also given.
關鍵字
語言英文
ISSN0024-3795;1873-1856
期刊性質國外
收錄於SCI
產學合作
通訊作者
審稿制度
國別美國
公開徵稿
出版型式紙本
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