MTL-algebras arising from partially ordered groups

After dropping the implication-like operation and reversing the order, an MTL-algebra becomes a partially ordered structure ( L ; ≤ , ⊕ , 0 , 1 ) based on the single addition-like operation ⊕ . Furthermore, ⊕ may be restricted to a partial, but cancellative addition + without loss of information. We deal in this paper with the case that the resulting partial algebra ( L ; ≤ , + , 0 , 1 ) is embeddable into the positive cone of a partially ordered group. It turns out that most of the examples of MTL-algebras known at present can be represented in this way. So the systematisation of a considerable class of MTL-algebras is achieved, and the methods of their construction are brought onto a common line.