On the semiring of cone preserving maps

doi:10.1016/0024-3795(81)90267-6

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/41393

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題名:	On the semiring of cone preserving maps
作者:	Tam, Bit-shun
貢獻者:	淡江大學數學學系
日期:	1981-02
上傳時間:	2010-01-28 07:27:32 (UTC+8)
出版者:	New York : Elsevier Inc.
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.
關聯:	Linear Algebra and Its Applications 35, pp.79-108
DOI:	10.1016/0024-3795(81)90267-6
顯示於類別:	[數學學系暨研究所] 期刊論文

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