| 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 | en |
| ISSN | 0024-3795 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 | USA |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41393 ) |
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