• Abstract Bivariant Cuntz Semigroups 

      [OWP-2017-04] Antoine, Ramon; Perera, Francesc; Thiel, Hannes (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-13)
      We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $((S,T))$ playing the role of morphisms from $S$ to $T$. Applied ...
    • Dominance and Transmissions in Supertropical Valuation Theory 

      [OWP-2011-07] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (Mathematisches Forschungsinstitut Oberwolfach, 2011)
      This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of ...
    • Monoid valuations and value ordered supervaluations 

      [OWP-2011-17] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (Mathematisches Forschungsinstitut Oberwolfach, 2011)
      We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ...
    • New representations of matroids and generalizations 

      [OWP-2011-18] Izhakian, Zur; Rhodes, John L. (Mathematisches Forschungsinstitut Oberwolfach, 2011)
      We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ...
    • Supertropical semirings and supervaluations 

      [OWP-2010-05] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (Mathematisches Forschungsinstitut Oberwolfach, 2010)
      We interpret a valuation $\upsilon$ on a ring $R$ as a map $\upsilon:R \rightarrow M$ into a so called bipotent semiring $M$ (the usual max-plus setting), and then define a supervaluation $\varphi$ as a suitable map into ...