Multiplicative Riesz decomposition on the ring of matrices over a totally ordered field
The Riesz Decomposition Theorem for lattice ordered groups asserts that when G is an l-group and when a nonnegative element a is bounded by a product of nonnegative elements b1,...,bn, then a can be decomposed into a product of nonnegative elements b'1,...,b'n, i.e., a = b'1·...·b' n, with the property that b'i ≤ bi for any i = 1,...,n. In this work we characterize all nonnegative matrices for which this decomposition is possible with respect to matrix multiplication. In addition, we show that this result can be applied to ordered semigroups.
Urenda Castaneda, Julio Cesar, "Multiplicative Riesz decomposition on the ring of matrices over a totally ordered field" (2009). ETD Collection for University of Texas, El Paso. AAI1465765.