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ScienceAsia 42(2016): 362-365 |doi: 10.2306/scienceasia1513-1874.2016.42.362

Zero divisors for matrices over commutative semirings

Asmaa M. Kanan

ABSTRACT:     It is known that a square matrix A over a commutative ring R with identity is a left or right zero divisor in Mn(R) if and only if the determinant of A is a zero divisor in R. Additively inverse commutative semirings with zero 0 and identity 1 are a generalization of commutative rings with identity. In this paper, we present some results for matrices over this type of semiring which generalize the above result for matrices over commutative rings.

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University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Beograd, Serbia

* Corresponding author, E-mail: asmaakanan@yahoo.com

Received 12 Feb 2013, Accepted 16 Oct 2013