The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...

Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP, where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is related to the coord...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.

‎generalizing the notion of character amenability for banach‎ ‎algebras‎, ‎we study the concept of $varphi$-connes amenability of‎ ‎a dual banach algebra $mathcal{a}$ with predual $mathcal{a}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{a}$ onto $bbb c$‎ ‎that lies in $mathcal{a}_*$‎. ‎several characterizations of‎ ‎$varphi$-connes amenability are given‎. ‎we also prove that the‎ ‎follo...

For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems proved by authors in 2017. In this study, homomorphism between algebras is defined, function examined then congruence relations are defined algebra. First third isomorphism introduced.