We prove the conjecture of Berstein, Hilton, and Ganea that an (n I)-connected CW-complex X with dim X < k(n 2) + 3 which has a co-Ak_,-space structure desuspends. Moreover, we show the following dual of a result of Segal: given a cosimplicial space Y, which is special in the sense that the canonical maps Vz’, Yr + k;, are homotopy equivalences and Yl is 2-connected then there is a functorial d...

In this paper, we show the existence of attached comultiplication structure on $\operatorname{Hom}_{eAe}(eA,D(Ae))$ if an $(eAe,A)$-bimodule $eA$ has double centraliser property over algebra $A$ with idempotent $e$. Then apply it gendo-Gorenstein algebras. As applications, give a sufficient and necessary condition for to be Gorenstein, bocs-theoretic characterisation property.

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coprod...

Our investigation in the present paper is based on three important results. (1) In [14], Ringel introduced Hall algebra for representations of a quiver over finite fields and proved elements corresponding to simple satisfy quantum Serre relation. This gives realization nilpotent part group if type. (2) [6], Green found homological formula representation category equipped Ringel's with comultipl...