A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian Gk(C ) as a ring of operators on the exterior algebra of a free module of rank n. Classical Pieri’s formula can be interpreted as Leibniz’s rule enjoyed by special Schubert cycles with respect to the wedge product.

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...

Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15

Based on a description of the squares of cofinite primary ideals of A + α (D), we prove the following results: for α ≥ 1, there exists a derivation from A + α (D) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m ∈ N and α ∈ [m, m + 1), every finite-dimensional extension of A + α (D) splits algebraically if and only if α ≥ m + 1/2.

Let V be an l-dimensional Euclidean space. Let G ⊂ O(V ) be a finite irreducible orthogonal reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H ∈ A choose αH ∈ V ∗ such that H = ker(αH). For each nonnegative integer m, define the derivation module D(A) = {θ ∈ DerS | θ(αH) ∈ SαmH}. The module is known to be a free S-module of...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

An enhancement to modular languages called module embedding facilitates the development and utilization of secure generic parallel algorithms.

An enhancement to modular languages called module embedding facilitates the development and utilization of secure generic parallel algorithms.

Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsio...