Invertible and nilpotent matrices over antirings

Details Invertible and nilpotent matrices over antirings Invertible and nilpotent matrices over antirings

2008-06-18

arxiv.org/abs/0806.2996v2

Mathematics

Commutative Algebra

9 pages, 1 figure, minor changes

Scientific paper

In this paper we characterize invertible matrices over an arbitrary commutative antiring S and find the structure of GL_n (S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent $n \times n$ matrix over an entire antiring can be written as a sum of $\lceil \log_2 n \rceil$ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum.

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