Non-Unique Factorizations of Upper Triangular Matrices
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While factorization in commutative semigroups has been well-studied, very little literature exists concerning factorization in the non-commutative setting. Given an atomic integral domain D, we will discuss factorization in Tn(D), the semigroup of n n upper triangular matrices having nonzero determinate with operation given by usual matrix multiplication. In particular, we will compute several important factorization-theoretic invariants that appear widely in the literature on commutative semigroups.