A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of \category with nite products". To capture such distinctions, we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical deenition of \essentially unique" and investigating its consequences. We call such 2-monads pr...

This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a brief survey of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of the traditional Functional Analysis and its idempotent version is discussed in the spirit of N. Bohr’s correspondence p...

In this paper, some known results about the functorial properties of Fourier–Stieltjes algebra, B(G), will be generalized. First all, idempotent theorem on algebra promoted and linked to p-analog one. Next, $$\pi$$ -Fourier space introduced by Arsac given, taking advantage theory ultrafilters, connection between dual p-pseudofunctions fully investigated. As main result, one significant applicab...

1. Introduction. Idempotent Mathematics is based on replacing the usual arithmetic operations by a new set of basic operations (e.g., such as maximum or minimum), that is on replacing numerical fields by idempotent semirings and semifields. Typical (and the most common) examples are given by the so-called (max, +) algebra R max and (min, +) algebra R min. Let R be the field of real numbers. The...

We study idempotents in intensional Martin-Löf type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky’s univalence axiom, there exist idempotents that do not split; thus in plain MLTT not all idempotents can be proven to split. On the other hand, assuming only function extensionality, an idempotent can b...

‎in a recent paper c‎. ‎miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{m}_n(mathbb{r})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎but the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎in this work we close the problem showing that also in this case the diameter is $4$.

Idempotent matrices play a significant role while dealing with different questions in matrix theory and its applications. It is easy to see that over a field any idempotent matrix is similar to a diagonal matrix with 0 and 1 on the main diagonal. Over a semiring the situation is quite different. For example, the matrix J of all ones is idempotent over Boolean semiring. The first characterizatio...

Let M be a right R-module. We call M Rad-H-supplemented iffor each Y M there exists a direct summand D of M such that(Y + D)/D (Rad(M) + D)/D and (Y + D)/Y (Rad(M) + Y )/Y .It is shown that:(1) Let M = M1M2, where M1 is a fully invariant submodule of M.If M is Rad-H-supplemented, thenM1 andM2 are Rad-H-supplemented.(2) Let M = M1 M2 be a duo module and Rad--supplemented. IfM1 is radical M2-...

Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct...

Abstract. In this paper, intuitionistic fuzzy h-bi-ideals and intuitionistic fuzzy hquasi-ideals of hemirings are studied and some related properties are investigated. We characterize fully idempotent hemirings by the properties of their intuitionistic fuzzy h-ideals.We also characterize h-hemiregularity, h-intra-hemiregularity and h-quasi-hemiregularity in hemirings by the properties of their ...