Geodesic
Unique prime factorization in a partial semigroup of matrix-polynomials
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 1, pp. 21-43.

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We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.
Keywords: partial semigroup, unique prime factorization 
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Kaltenbäck, Michael; Woracek, Harald. Unique prime factorization in a partial semigroup of matrix-polynomials. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 1, pp. 21-43. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_1_a1/

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