半群环的幂等元

讨论了半群环R[S]的幂等元问题．对[1]提出的公开问题9作了一个肯定回答，同时就一般半群环的幂等元的具体形式作了深入的研究，给出了若干情形下的幂等元刻划．     

Inner Generalized Inverses with Prescribed Idempotents

We define and characterize inner generalized inverses with prescribed idempotents. These classes of generalized inverses are natural algebraic extension of generalized inverses of linear operators with prescribed range and kernel. We consider the reverse order rule for inner generalized inverses of elements of a ring, some perturbation bounds, and we construct an iterative method for computing a (p, q)-inner inverse in Banach algebras.     

Additive Mappings Preserving Rank-one Idempotents

A complete characterization of additive mappings φ ： B（X）→B（Y）, which map rank-one idempotents to themselves or to zero, is given.     

Multiplicative Mappings of Rings

Let R and F be arbitrary associative rings. A mapping φ of R onto F is called a multiplicative isomorphism if φ is bijective and satisfies φ（xy） = φ（x）φ（y） for all x, y ∈ R. In this short note, we establish a condition on R, in the case where R may not contain any non-zero idempotents, that assures that φ is additive, which generalizes the famous Martindale＇s result. As an application, we show that under a mild assumption every multiplicative isomorphism from the radical of a nest algebra onto an arbitrary ring is additive.     

Centers with degenerate infinity and their commutators

We study polynomial systems with degeneracy at infinity and a center-focus equilibrium at the origin. We give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and, also, we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form. Finally, we characterize the systems (−y+P_s+∑_j=kⁿ⁻¹xH_j,x+Q_s+∑_j=kⁿ⁻¹yH_j)^t with polynomial commutator, with P_j,Q_j,H_j and K_j homogeneous polynomials.     

LP（Rn）-Boundedness of certain commutators

In this paper, the Lp(Rn)-boundedness of the commutators generalized by BMO(Rn) function and the singular integral operator T with rough kernel Ω∈ Llog+ L(Sn-1) is proved by using the Bony's formula for the paraproduct of two functions.     

Products of projections in von Neumann algebras

We describe the elements of von Neumann algebras which can be represented as products of orthogonal projections and idempotents, and estimate the minimal number of terms in the product.     

Polyadic codes of prime power length

Polyadic codes constitute a special class of cyclic codes and are generalizations of quadratic residue codes, duadic codes, triadic codes, m-adic residue codes and split group codes, which have good error-correcting properties. In this paper, we give necessary and sufficient conditions for the existence of polyadic codes of prime power length. Examples of some good codes arising from the family of polyadic codes of prime power length are also given.     

Powers of commutators

Any element of a finite group that generates the same cyclic subgroup as some commutator, is itself a commutator. The paper presents a completely elementary proof of this fact, whereas previous proofs depend on character theory.     

Weighted estimates for singular integral operators and commutators associated with the sections

In this paper we prove weighted estimates for singular integral operators and commutators associated with the sections.     

CRW型交换子在Triebel-Lizorkin空间的有界性

本文考虑交换子[b,T]在 Triebel-Lizorkin 空间上的有界性,其中 b∈BMO(R~n),T 是卷积型奇异积分算子,其核为Ω∈L log~ L(S~(n-1)),给出了该交换子在 F_p~(s,p)(R~n)(s＞0,1＜p,q＜∞) 上有界的一个等价条件．     

An algebraic invariant for Jordan automorphisms on β(<Emphasis Type="Italic">H</Emphasis>): The set of idempotents

Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT ^-1 for all A ∈ B(H), or Φ(A) = TA*T ^-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism.     

Boundedness of certain commutators on Triebel–Lizorkin spaces

In this paper, two types of commutators are considered, and the boundedness of these operators on Triebel–Lizorkin spaces are discussed.     

Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(x−1)

Let q be an odd prime power and p be an odd prime with gcd(p,q)=1. Let order of q modulo p be f, and q^f=1+pλ. Here expressions for all the primitive idempotents in the ring R_pⁿ=GF(q)[x]/(x^pn−1), for any positive integer n, are obtained in terms of cyclotomic numbers, provided p does not divide λ if n2. The dimension, generating polynomials and minimum distances of minimal cyclic codes of length pⁿ over GF(q) are also discussed.     

Idempotent Generation in the Endomorphism Monoid of a Uniform Partition

Denote by 𝒯_n and 𝒮_n the full transformation semigroup and the symmetric group on the set {1,…, n}, and ?_n = {1} ∪ (𝒯_n?𝒮_n). Let 𝒯(X, 𝒫) denote the monoid of all transformations of the finite set X preserving a uniform partition 𝒫 of X into m subsets of size n, where m, n ≥ 2. We enumerate the idempotents of 𝒯(X, 𝒫), and describe the submonoid S = ? E ? generated by the idempotents E = E(𝒯(X, 𝒫)). We show that S = S₁ ∪ S₂, where S₁ is a direct product of m copies of ?_n, and S₂ is a wreath product of 𝒯_n with 𝒯_m?𝒮_m. We calculate the rank and idempotent rank of S, showing that these are equal, and we also classify and enumerate all the idempotent generating sets of minimal size. In doing so, we also obtain new results about arbitrary idempotent generating sets of ?_n.     

Commutators of hardy type operators on Herz spaces with variable exponents北大核心CSCD

We mainly prove the boundedness of the commutators of Hardy type operators on Herz spaces Kp(·),qα(·), where α(·) and p(·) are both variable. ©, 2015, Chinese Academy of Sciences. All right reserved.