This paper is devoted to irreducible radical field extensions, i.e., extensions that can be obtained by adjunction of roots binomials. We find a criterion for cyclotomic radical. developes the Gauss–Wantzel theorem about constructible polygons. also prove any normal solvable extension some K until has all unity. generalizes Abel’s theorem, which fills gap in uncomplete Ruffini proof impossibili...

in this paper, we give a classification of non simply connected seven dimensional reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. we characterize the acting groups and describe the orbits. the first and second homo-topy groups of the orbits have been presented as well.

we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...