Miriam Cohen raised the question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple Hopf algebra is semiprime. In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra for...

It is shown that the classification theorems for semisimple algebraic groups in characteristic zero can be derived quite simply and naturally from the corresponding theorems for Lie algebras by using a little of the theory of tensor categories. This article is extracted from Milne 2007. Introduction The classical approach to classifying the semisimple algebraic groups over C (see Borel 1975, §1...

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-...

We prove an analogue of the Lp version of Hardy’s theorem on semisimple Lie groups. The theorem says that on a semisimple Lie group, a function and its Fourier transform cannot decay very rapidly on an average.

Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to realm topological with right linear topology, we show that abelian category left contramodules over such a ring is split (equivalently, semisimple) if and only discrete modules same semisimple). Our results in this direction complement those Iovanov-Mesyan-Reyes. An extension Bass perfect formulated as list c...