in this paper, applying the concept of generalized a-valued norm on a right h  - module and also the notion of ϕ-homomorphism of finsler modules over c  -algebras we rst improve the denition of the finsler module over h  -algebra and then dene ϕ-morphism of finsler modules over h  -algebras. finally we present some results concerning these new ones.

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

We define a nontrivial homomorphism from the Hecke algebra of type B onto a reduced algebra of the Hecke algebra of type A at roots of unity. We use this homomorphism to describe semisimple quotients of the Hecke algebra of type B at roots of unity. Using these quotients we determine subfactors obtained from the inclusion of Hecke algebra of type A into Hecke algebras of type B. We also study i...

Let CRF S denote the category of S-colored rooted forests, and HCRFS denote its Ringel-Hall algebra as introduced in [6]. We construct a homomorphism from a K+ 0 (CRF S)–graded version of the Hopf algebra of noncommutative symmetric functions to HCRFS . Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a K+ 0 (CRF S)–graded version of the algebra of quasisymmetric func...

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...

We prove the existence of a homomorphism vertex algebras, from vacuum Verma module over loop algebra an untwisted affine algebra, whose construction is analogous to that Feigin-Frenkel at critical level algebra.

‎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...

If H is a commutative connected graded Hopf algebra over a commutative ring k, then a certain canonical k-algebra homomorphism H → H⊗QSymk is defined, where QSymk denotes the Hopf algebra of quasisymmetric functions. This homomorphism generalizes the “internal comultiplication” on QSymk, and extends what Hazewinkel (in §18.24 of his “Witt vectors”) calls the Bernstein homomorphism. We construct...

A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.