PI-algebras and their cocharacters

Nil, nilpotent and PI-algebras

The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in the ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. Howev...

Smarandache algebras and their subgroups

In this paper we define S algebras and show that every finite group can be found in some S algebra.  We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.

Rational Group Actions on Affine Pi-algebras

Let R be an affine PI-algebra over an algebraically closed field k and let G be an affine algebraic k-group that acts rationally by algebra automorphisms on R. For R prime and G a torus, we show that R has only finitely many G-prime ideals if and only if the action of G on the center of R is multiplicity free. This extends a standard result on affine algebraic G-varieties. Under suitable hypoth...

Algebras and Their Arithmetics

Algebras and Their Unified

We give a complete classification of the real forms of simple nonlinear superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and present a unified realization of these algebras with simple symmetry groups. This classification is achieved by establishing a correspondence between simple nonlinear QSCA’s and SCA’s and quaternionic and superquaternionic symmetric spaces of simple ...