A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-representation of $Gamma$-so-rings.

Keywords: Subdirectly irreducible $Gamma$-so-ring, Subdirect product, $(phi, rho)$-product of $Gamma_i$-so-rings, $(phi, rho)$-representation of a $Gamma$-so-ring.

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