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Structures of idempotent matrices over chain semirings
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Abstract
In this paper, we have characterizations of idempotent matri-ces over general Boolean algebras and chain semirings. As a consequence,we obtain that a fuzzy matrix A = [ai;j ] is idempotent if and only if allai;j -patterns ofA are idempotent matrices over the binary Boolean alge-bra B1 = f0;1g. Furthermore, it turns out that a binary Boolean matrixis idempotent if and only if it can be represented as a sum of line partsand rectangle parts of the matrix.
참고문헌 (7)
- R. B. Bapat, "Nonnegative idempotent matrices and minuspartial order", 261, pp.143~154 (1997)
- Beasley, "Linear operators strongly preserving idempotent ma-trices over semirings" (1992)
- J. S. Golan, "Semirings and their applications, updated and expanded version of the oryof semirings, with applications to mathematics and theoretical computer science" (1999), KluwerAcademic Publishers, Dordrecht
- Kirkland, "Linear operators preserving invariants of non-binarymatrices", pp.3~4 (1993)
- V. N. Kolokoltsov, "Idempotent Analysis and its Applications", 401 (1997), Dordrecht: Kluwer Academic Publishers
- S. Z. Song, "Types and enumeration of idempotent matrices", 2(6), pp.1029~1042 (2001)
- S. Z. Song, "Idempotent matrix preservers over Booleanalgebras", 44(1), pp.169~178 (2007)
관련 논문AI추천
A Note on Regularity in Matrix SemiringsShamik Ghosh경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제1호Idempotent matrix preservers over Boolean algebras강경태, 송석준, LeRoy B. Beasley대한수학회 · 대한수학회지2007 · 제44권 제1호Rank-preserver of Matrices over Chain Semiring강경태, Seok-Zun Song경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제1호A Note on Regular Ternary SemiringsSukhendu Kar, Tapan Kumar Dutta경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호On Partitioning Ideals of SemiringsJayprakash Ninu Chaudhari, Vishnu Gupta경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제2호Factor Rank Comparisons of Matrices over Two Related Semirings송석준대한수학회 · 대한수학회논문집2006 · 제21권 제2호
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