Semigroup Forum

, Volume 65, Issue 1, pp 71–82 | Cite as

Triangular norms as ordinal sums of semigroups in the sense of A. H. Clifford

  • E. P. KlementEmail author
  • R. Mesiar
  • E. Pap
Research Article


Ordinal sums of semigroups in the sense of [3] leading to triangular norms [29] are studied, generalizing the ordinal sum of triangular norms [30]. The summands of these general ordinal sums are fully characterized, and the ordinal irreducibility of triangular norms is investigated, inducing a natural partition of the class of all triangular norms.


Zero Divisor Neutral Element Topological Semigroup Usual Order Triangular Norm 
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Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  1. 1.Department of Algebra, Stochastics and Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria
  2. 2.Department of Mathematics and Descriptive Geometry Faculty of Civil EngineeringSlovak Technical UniversityBratislavaSlovakia
  3. 3.Institute of Information Theory and AutomationCzech Academy of SciencesPrague 8Czech Republic
  4. 4.Institute of MathematicsUniversity of Novi SadNovi SadYugoslavia

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