The algebraic structure of the set of doubly stochastic circulants is that of a semi-ring. The concept of a prime in the doubly stochastic circulants is introduced in this paper and examples are given. The classification of a prime in the doubly stochastic circulants is equivalent to the solvability of a linear equation over a doubly stochastic circulant. A representation of doubly stochastic circulants as polynomials in the quotient semi-ring of $R_+[z]$ is presented.

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CWI
Department of Operations Research, Statistics, and System Theory [BS]
System and control theory

Picci, G, van den Hof, J.M, & van Schuppen, J.H. (1995). Primes in the doubly stochastic circulants. Department of Operations Research, Statistics, and System Theory [BS]. CWI.