we prove that the class of profinite groups $g$ that have a factorization $g=ab$‎ ‎with $a$ and $b$ abelian closed subgroups‎, ‎is closed under taking inverse limits‎ ‎of surjective inverse systems‎. ‎this is a generalization of a recent result by k. h. hofmann and f. g. russo‎. ‎as an application we reprove their generalization of iwasawa's structure theorem for‎ ‎quasihamiltonian pro-$p$...

Upper bounds on the CP asymmetry relevant for leptogenesis are reexamined and found weaker than in previous literature, both for hierarchical and for quasi-degenerate righthanded neutrinos. Successful leptogenesis implies the usual lower bound on right-handed neutrino masses, and an upper bound on left-handed neutrino masses (which we obtain to be 0.15 eV at 3σ) only if right-handed neutrinos a...

In this paper, we prove that some stabilizing controllers of a plant, which admits a left/right-coprime factorization, have a special form where their stable and unstable parts are separated. The dimension of the unstable part depends on the algebraic concept of stable range of the ring A of SISO stable plants. Moreover, we prove that, if the stable range of A is equal to 1, then every plant—de...

A factorization system (E ,M) on a category A gives rise to the covariant category-valued pseudofunctor P of A sending each object to its slice category over M. This article characterizes the P so obtained as follows: their object images have terminal objects, and they admit bicategorically cartesian liftings, up to equivalence, of slice-category projections. It is clear that, and how, (E ,M) c...

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...

Notions of strongly regular, regular and left(right) regular $Gamma$−semigroupsare introduced. Equivalent conditions are obtained through fuzzy notion for a$Gamma$−semigroup to be either strongly regular or regular or left regular.