Prime ideals of ore extensions

For the Ore extension R[t, S,D], where R is a prime ring, we describe prime having zero intersection with R.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

Prime ideals in Hopf galois extensions

For a finite-dimensional Hopf algebraH, we study the prime ideals in a faithfully flatH-Hopf-Galois extensionR ⊂A. One application is to quotients of Hopf algebras which arise in the theory of quantum groups at a root of 1. For the Krull relations betweenR andA, we obtain our best results whenH is semisolvable; these results generalize earlier known results for crossed products for a group action and for algebras graded by a finite group. We also show that ifH is semisimple and semisolvable, thenA is semiprime providedR isH-semiprime.     

Prime extensions and categoricity in power

This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models. Author working on Ph. D. thesis under supervision of Prof. M. O. Rabin. Author working at the CNRS under the supervision of Prof. D. Lacombe.     

Classification of extensions of torus algebra II

We use extension theory and algebraic methods to give a complete characterization of extensions of torus algebra by stable Cuntz algebras,and prove certain classification theorems of these extension algebras.     

Derivations and extensions of lie color algebra

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.     

A Prime Ideal Principle in commutative algebra

In this paper, we offer a general Prime Ideal Principle for proving that certain ideals in a commutative ring are prime. This leads to a direct and uniform treatment of a number of standard results on prime ideals in commutative algebra, due to Krull, Cohen, Kaplansky, Herstein, Isaacs, McAdam, D.D. Anderson, and others. More significantly, the simple nature of this Prime Ideal Principle enables us to generate a large number of hitherto unknown results of the “maximal implies prime” variety. The key notions used in our uniform approach to such prime ideal problems are those of Oka families and Ako families of ideals in a commutative ring, defined in (2.1) and (2.2). Much of this work has also natural interpretations in terms of categories of cyclic modules.     

Coalgebra extensions and algebra coextensions of galois type

The notion of a coalgebra-Galois extension is defined as a natural generalisation of a Hopf-Galois extension. It is shown that any coalgebra-Galois extension induces a unique entwining map ψ compatible with the right coaction. For the dual notion of an algebra-Galois coextension it is also proven that there always exists a unique entwining structure compatible with the right action.     

Commutative Abelian Galois extensions of a Banach algebra

Let A be a commutative unital Banach algebra with connected maximal ideal space X. We show that the Gelfand transform induces an isomorphism between the group of commutative Galois extensions of A with given finite Abelian Galois group, and the corresponding group of extensions of C(X). This result is applied, when X is sufficiently nice, to construct a separable projective finitely generated faithful Banach A-algebra whose maximal ideal space is a given finitely fibered covering space of X.     

Length two extensions of modules for the Witt algebra

In this paper, we establish an explicit classification of length two extensions of tensor modules for the Witt algebra using the cohomology of the Witt algebra with coe?cients in the module of the space of homomorphisms between the two modules of interest. To do this we extended our module to a module that has a compatible action of the commutative algebra of Laurent polynomials in one variable. In this setting, we are be able to directly compute all possible 1-cocycles.     

Bosonic and fermionic representations of Lie algebra central extensions

Given any representation of an arbitrary Lie algebra g over a field K of characteristic 0, we construct representations of a central extension of g on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in H²(g;K). We illustrate these techniques with several concrete examples.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

An arithmetic obstruction to division algebra decomposability

This paper presents an indecomposable finite-dimensional division algebra of -power index that decomposes over a prime-to- degree field extension, obtained by adjoining -th roots of unity to the base. This shows that the theory of decomposability has an arithmetic aspect.