FACTORIZATION OF TRIANGULAR MATRICES OVER INFORMATION ALGEBRAS
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We define information algebras, i.e., antinegative semirings without zero-divisors, and explore their structure. We then generalize results from the paper On upper triangular nonnegative matrices by Chen et al. (2015) by considering factorization in the semiring of upper triangular matrices with entries in an information algebra. In particular, we provide a classification of the atoms of this semiring in terms of both the additive and multiplicative structure of the underlying information algebra. We conclude with results on the maximum and minimum factorization lengths of such matrices, as well as other factorization-theoretic invariants.