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Abstract:
An antiring is a semiring which is zerosumfree (i.e., a + b = 0 implies a = b = 0 for any a, b in this semiring). In this paper, we study the nilpotency of matrices over commutative antirings. We first provide some properties and characterizations of the nilpotent matrices in terms of principal permanental minors, main diagonals and permanental adjoint matrices. When a family of matrices are simultaneously considered, we establish some characterizations of the simultaneous nilpotence for a family of matrices. (C) 2010 Elsevier Inc. All rights reserved.
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LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN: 0024-3795
Year: 2010
Issue: 8-10
Volume: 433
Page: 1541-1554
1 . 0 0 5
JCR@2010
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JCR@2023
ESI Discipline: MATHEMATICS;
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 5
SCOPUS Cited Count: 6
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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