Abstract
1. Preliminaries. A structure A = 〈A, ·, 1,≤〉 is a partially ordered monoid if 〈A, ·, 1〉 is a monoid, ≤ is a partial order on A, and for all x, y, z ∈ A, if x ≤ y, then x · z ≤ y · z and z · x ≤ z · y. A is integral if x ≤ 1, for all x ∈ A. Finally, A is residuated if for all x, y ∈ A the set {z : z · x ≤ y} contains a largest element, called the residual of x relative to y, and denoted by x → y. A partially ordered commutative, residuated and integral monoid 〈A, ·, 1,≤〉 can be treated as an algebra 〈A, ·,→, 1〉, since the partial order ≤ can be recovered via x ≤ y iff x → y = 1. We will refer to the algebras thus obtained by the acronym pocrim. The class M of all pocrims is a quasivariety definable by:
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