In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

This paper continues the investigation of the rst author begun in part one. The hereditary properties of n-homomorphism amenability for Banach algebras are investigated and the relations between n-homomorphism amenability of a Banach algebra and its ideals are found. Analogous to the character amenability, it is shown that the tensor product of two unital Banach algebras is n-homomorphism amena...

In this paper we introduce a generalization of M-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . We will use the structure of the radical of a module in  and get some suitable results about this class of modules. Also the relation between injective hull in  and this kind of modules will be investigated in this article.   For a module  we show...

1. I n t r o d u c t i o n 1. Let M be a real-analytic manifold, Vect M the Lie algebra of analytic vector fields on M. We consider a vector field f E Vect M as a differential operator of first order on the algebra of smooth functions C ~ (M) which satisfies the differentiation rule f(W1W2) -" (fw1)W2 + wI(fW2) VWI, W2 E Coo(M). A point z E M will be identified with the corresponding homomorphi...

Let φ : (R, m)→ (S, n) be a local homomorphism of commutative noetherian local rings. Suppose that M is a finitely generated S-module. A generalization of Grothendieck’s non-vanishing theorem is proved for M (i.e. the Krull dimension of M over R is the greatest integer i for which the ith local cohomology module of M with respect to m, Hi m(M), is non-zero). It is also proved that the Gorenstei...

We prove that every MV-effect algebra M is, as an effect algebra, a homomorphic image of its R-generated Boolean algebra. We characterize central elements of M in terms of the constructed homomorphism. 1. Definitions and basic relationships An effect algebra is a partial algebra (E;⊕, 0, 1) with a binary partial operation ⊕ and two nullary operations 0, 1 satisfying the following conditions. (E...

Let M be a free finitely generated Z-module with basis B and ∆M the kernel of the homomorphism M → Z which maps B to 1. A basis of ∆M can be easily constructed from the basis B of M . Let further R be a submodule of M such that N = M/R is free. The subject of investigation is the module ∆N = (∆M + R)/R. We compute the index [N : ∆N ] and construct bases of ∆N with the help of a basis of N . Fin...

An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...

A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism f : G → H. A classic problem is to characterize the family of homomorphic preimages of a given graph H. A geometric graph G is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position A geometric homomorphism (resp. ...