A singular primitive ring

The primitive idempotents of the p-permutation ring

Let G be a finite group, let p be a prime number, and let K be a field of characteristic 0 and k be a field of characteristic p, both large enough. In this note we state explicit formulae for the primitive idempotents of K ⊗Z ppk(G), where ppk(G) is the ring of p-permutation kG-modules. AMS Subject Classification : 19A22, 20C20.

Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation

We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) iψt(t,x)− ψ + |ψ |2σψ = 0, x ∈ R , 4/d σ 4. These solutions collapse with the quasi-self-similar ring profile ψQB , where |ψQB(t, r)| ∼ 1 L2/σ (t) QB ( r − rmax(t) L(t) ) , r = |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ∼ r0L(t) is the ring radius, and α = (4 − σ)/(σ (d − 1)). The blo...

A Topology for the Set of Primitive Ideals in an Arbitrary Ring.

Primitive Neuroectodermal Tumor (PNET) ofKidney -A Rare Entity

Primitive  neuroectodermal  tumor  (PNET)  of  kidney  is  an  extremely  rare  renal  neoplasm  with only about fifty reported cases in literature.  Presumably,of neural crest origin, these tumors behave  aggressively  and  carry  a  poor prognosis.  We  report  a  case  of  22-year  old  female  patient complaining of left loin pain with recurrent hematuria for last 3 months. On clinical ex...

A Note on a graph associated to a commutative ring

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...