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Baer semirings and Baer ∗-semirings of cone-preserving maps

✍ Scribed by George Phillip Barker; Bit-Shun Tam

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
835 KB
Volume
256
Category
Article
ISSN
0024-3795

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✦ Synopsis

The study of 7r(K), the semiring of matrices which leave invariant the proper cone K, is continued in this paper. The definitions of Baer rings and Baer * -rings are extended to semirings, at least in the case of 7r(K). Results that relate the concepts of right (left) annihilators, right (left) facial ideals, and p-exposed or o.p.-exposed faces are given. Proper cones K for which 7r(K) is a right (left) Baer semiring or a Baer • -semiring are characterized. In particular, it is shown that ~r(K) is a Baer *-semiring if and only if K is a perfect cone. The set of projections in 7r(K) is investigated, and its lattice structure is analyzed. The concepts of equivalence of idempotents and • -equivalence of projections in ~'(K) are introduced and examined.

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