We answer a question posed in [4], and demonstrate that in general Rickard modules in relatively stable categories are not idempotent modules even if one localizes with respect to a tensor ideal subcategory. We also show that there is a modification one can make so as to recover the idempotent

Abstract Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's omega operator and a divergence operator. They are determined for various computational models, and conditions for their existence and their coincidence are given. It turns out

Abstract. We study and compare two notions of non-termination on idempotent semirings: infinite iteration and divergence. We determine them in various models and develop conditions for their coincidence. It turns out that divergence yields a simple and natural way of modelling infinite behaviour

Abstract. We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected CW-complexes, some of which extend P-local-ization of nilpotent spaces, at a set of primes P. We focus our attention on one such functor, whose local objects are CW-complexes X

of idempotent group dioids) for which one can mimic the token game of Petri nets to define the behaviour of these generalized Petri nets whose flow relations and place contents are valued in the closed monoidal structure. 1

Abstract We have initiated the study of nets with bicomplex entries. Due to the multi dimensionality of the bicomplex space there arise different types of tendencies called confinements. The bicomplex space equipped with real order topology as well as idempotent order topology exhibits interesting

Abstract. When merging belief functions, Dempster rule of combina-tion is justified only when sources can be considered as independent. When dependencies are ill-known, it is usual to ask the merging opera-tion to satisfy the property of idempotence, as this property ensures a cautious behaviour

Five algebraic notions of termination are formalised, analysed and compared: well-foundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward

Nondeterminism is a direct outcome of interactions and is, therefore a central ingredient for modelling concurrent systems. Trees are very useful for modelling nondeterministic behaviour. We aim at a tree-based interpretation of regular expressions and study the effect of removing the idempotence

Recently, applications of higher-dimensional (hypercomplex) algebras (e.g. quater-nions, Clifford algebras) to Digital Signal Processing (DSP) emerge. Some of these em-ployed algebras comprise idempotent and nilpotent elements. Regarding the latter, the consequences for DSP applications