Geodesic
Semigroups of non-negative integral matrices
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 39-42

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In [1], Pall proved an interesting result on a certain class of 2 × 2 integral matrices. He showed that the semigroup of 2 × 2 matrices of determinant 1 and non-negative entries contains exactly 2 primes , and every other non-unit is expressible uniquely as products of these primes. Before formally stating this result, we need some notation. Let Gn denote the semigroup of n × n matrices with determinant 1 and nonnegative integral entries, In the n × n identity matrix, the n × n matrix with a 1 as its (i, j) element and zeros elsewhere, and let . When the dimension is clear, we shall drop the superscripts. 
Cordes, Craig M. Semigroups of non-negative integral matrices. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 39-42. doi: 10.1017/S0017089500002081
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[1] 1.Pall, Gordon, Binary quadratic and cubic forms and unipositive matrices; to appear in J. Number Theory. Google Scholar

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