Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

Unless we say otherwise, every vector space we talk about is taken to be over C. A Banach algebra is a Banach space A that is also an algebra satisfying ‖AB‖ ≤ ‖A‖ ‖B‖ for A,B ∈ A. We say that A is unital if there is a nonzero element I ∈ A such that AI = A and IA = A for all A ∈ A, called a identity element. If X is a Banach space, let B(X) denote the set of bounded linear operators X → X, and...

The hit problem for a cohomology module over the Steenrod algebra A asks for a minimal set of A-generators for the module. In this paper we consider the symmetric algebras over the field Fp, for p an arbitrary prime, and treat the equivalent problem of determining the set of A∗-primitive elements in their duals. We produce a method for generating new primitives from known ones via a new action ...

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

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.

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...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

In this article, we study the decomposition of weight–sl2n–modules of degree 1 to a dual pair (sl2, sln). We show that in some generic cases we have an explicit branching rule leading to a Howe–type correspondence between simple highest weight modules. We also give a Howe–type correspondence in the non–generic case. This latter involves some (non simple) Verma modules. Let g denote a reductive ...