REFLEXIVE PROPERTY ON IDEMPOTENTS

Commuting Idempotents, Square-free Modules, and the Exchange Property

We give a criterion for when idempotents of a ring R which commute modulo the Jacobson radical J(R) can be lifted to commuting idempotents of R. If such lifting is possible, we give extra information about the lifts. A “half-commuting” analogue is also proven, and this is used to give sufficient conditions for a ring to have the internal exchange property. In particular, we show that if R/J(R) ...

On concentrating idempotents, a survey

A sum of exponentials of the form f(x) = exp (2 iN1x)+exp (2 iN2x)+ +exp (2 iNmx), where the Nk are distinct integers is called an idempotent trigonometric polynomial or, simply, an idempotent. It is known that for every p > 1; and every set S of the torus T = R=Z with jSj > 0; there are idempotents concentrated on S in the Lp sense. We sketch how this concentration phenomenon originated as a r...

Heisenberg Idempotents on Unipotent Groups

Let G be a possibly disconnected algebraic group over an algebraically closed field k of characteristic p > 0, such that its neutral connected component, H = G0, is a unipotent group. We recall that an algebraic group over k is defined to be a smooth group scheme of finite type over k. Let us fix a prime number l 6= p. If X is a k-scheme, we use D(X) to denote the bounded derived category of Ql...

On bicyclic reflexive graphs

On reflexive subobject lattices and reflexive endomorphism algebras

In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.