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: <=, circle plus, 0, 1) based on the single addition-like operation circle plus. Furthermore, circle plus 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. (C) 2009 Elsevier B.V. All rights reserved.
mtl-algebra partially ordered group basic semihoop partial algebra associated to a basic semihoop