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2 results

  • LEVELS OF CANCELLATION FOR MONOIDS AND MODULES

  • Part of
  • PERE ARA, KEN GOODEARL, PACE P. NIELSEN, KEVIN C. O’MEARA, ENRIQUE PARDO, FRANCESC PERERA
  • Journal:
    Journal of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    14 November 2025, pp. 1-42
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  • Levels of cancellativity in commutative monoids M, determined by stable-rank values in $\mathbb {Z}_{> 0} \cup \{\infty \}$ for elements of M, are investigated. The behavior of the stable ranks of multiples $ka$, for $k \in \mathbb {Z}_{> 0}$ and $a \in M$, is determined. In the case of a refinement monoid M, the possible stable-rank values in archimedean components of M are pinned down. Finally, stable rank in monoids built from isomorphism or other equivalence classes of modules over a ring is discussed.

  • Archimedean components of triangular norms

  • Part of
  • Erich Peter Klement, Radko Mesiar, Endre Pap
  • Journal:
    Journal of the Australian Mathematical Society / Volume 78 / Issue 2 / April 2005
    Published online by Cambridge University Press:
    09 April 2009, pp. 239-255
    Print publication:
    April 2005
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  • The Archimedean components of triangular norms (which turn the closed unit interval into anabelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.