we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

In Possibilistic Decision Theory (PDT), decisions are ranked by a pessimistic or by an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la Von Neumann and Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la Von Ne...

The aim of this paper is to provide a unifying axiomatic justification for a class of qualitative decision models comprising among others optimistic/pessimistic qualitative utilities, binary possibilistic utility, likelihood-based utility, Spohn’s disbelief function-based utility. All those criteria that are instances of Algebraic Expected Utility have been shown to be counterparts of Expected ...

We have first demonstrated that Debreu’s view regarding the publication of The Theory of Games and Economic Behavior by von Neumann and Morgenstern in 1944 as the birth of modern mathematical economics is not convincing. In this paper, we have proposed the hypothesis that the coordinated research programs in the 1930’s, initiated by the Econometric Society and the Cowles Commission for Research...

Introduction. In 1960 a set of axioms for cooperative games without side payments was suggested by Aumann and Peleg [l] which provides a neat generalization of the classical von Neumann-Morgenstern «-person theory [S]. In subsequent papers [2], [3], and [4], many results parallel to the classical theory have been proven in this new framework. The purpose of this note is to re-examine the axioms...

This note uncovers new properties of the von Neumann-Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of the tournament game introduced by Laffond, Laslier and Le Breton (1993) [The bipartisan set of a tournament game....