Now showing items 1-7 of 7

• #### Dominance and Transmissions in Supertropical Valuation Theory ﻿

[OWP-2011-07] (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] (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] (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 linear algebra ﻿

[OWP-2010-14] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of "ghost surpasses." Special attention is paid to the various ...
• #### Supertropical Matrix Algebra III : Powers of Matrices and Generalized Eigenspaces ﻿

[OWP-2010-20] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power ...
• #### Supertropical Quadratic Forms I ﻿

[OWP-2013-27] (Mathematisches Forschungsinstitut Oberwolfach, 2013)
We initiate the theory of a quadratic form q over a semiring $R$. As customary, one can write $q(x+y)=q(x)+q(y)+b(x,y)$, where b is a companion bilinear form. But in contrast to the ring-theoretic case, the companion ...
• #### Supertropical semirings and supervaluations ﻿

[OWP-2010-05] (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 ...