Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

幂等矩阵线性组合的可逆性

设T1,T2,T3是三个不同的两两相互可交换的n×n非零的三次幂等矩阵,并且c1,c2,c3是非零数.本文主要给出了线性组合c1T1 c2T2 c3T3可逆性的刻画.     

Tensor products of idempotent semimodules. An algebraic approach

We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are expressed in purely algebraic terms. This is one of a series of papers on idempotent functional analysis. Dedicate to S. G. Krein on the occasion of his 80th birthday Translated fromMatermaticheskie Zametki, Vol. 65, No. 4, pp. 572–585, April, 1999.     

幂等左侧余Quantale的特征

更好地讨论Quantale这一崭新数学分支的各种性质;给出幂等余Quantale及幂等左侧余Quantale的定义;幂等左侧余Quantale既是子余Quantale又是商余Quantale;且其补集是简单余Quantale;幂等余Quantale具有和其他Quantale类似的一些性质,并且与简单余Quantale也...     

The structure of idempotent residuated chains

In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green’s relation on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains, we obtain some characterizations of subdirectly irreducible, simple and strictly simple idempotent residuated chains. This work is supported by a grant of NSF, China # 10471112 and a grant of Shaanxi Provincial Natural Science Foundation # 2005A15.     

Global determinism of idempotent semigroups

The power semigroup, or global, of a semigroup S is the set 𝒫(S) of all nonempty subsets of S equipped with the naturally defined multiplication. A class 𝒦 of semigroups is globally determined if any two members of 𝒦 with isomorphic globals are themselves isomorphic. The principal goal of this paper is to prove that the class of all idempotent semigroups is globally determined.     

The parallel refinement of weakening idempotent pair

In this paper, we invent the parallel refinement, which refines the weakening idempotent pair into the positive and contractive one preserving K-theory information. We conduct a quantitative matrix analysis for this refinement, which shows that this refinement is more effective when we derive almost projection from weakening idempotent pairs.     

The group inverse of the combinations of two idempotent matrices

In this article, we discuss the group inverse of aP + bQ + cPQ + dQP + ePQP + fQPQ + gPQPQ of idempotent matrices P and Q, where a, b, c, d, e, f, g ∈ ? and a ≠ 0, b ≠ 0, put forward its explicit expressions, and some necessary and sufficient conditions for the existence of the group inverse of aP + bQ + cPQ.     

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.     

The lattice of idempotent distributive semiring varieties

A solution is given for the word problem for free idempotent distributive semirings. Using this solution the latticeL (ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out thatL (ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the latticeL(B) of all band varieties. ThereforeL(ID) is countably infinite and distributive. Every subvariety of ID is finitely based. Project supported by the National Natural Science Foundation of China (Grant No. 19761004) and the Provincial Applied Fundamental Research Foundation of Yunnan (96a001z).     

On global periodicity of difference equations

In this research, we consider a difference equation of order k?2 of the following form:

     

关于两类含幺幂等元半环

研究了两类重要的含幺幂等元半环簇中成员的一些性质,给出了其中成员的等价刻画,并讨论了其中成员的结构,得到了这两类子簇中成员的一些结果．     

Homological behavior of idempotent subalgebras and Ext algebras

Let A be a(left and right) Noetherian ring that is semiperfect. Let e be an idempotent of A and consider the ring Γ :=(1-e)A(1-e) and the semi-simple right A-module Se := e A/e rad A. In this paper, we investigate the relationship between the global dimensions of A and Γ, by using the homological properties of Se. More precisely, we consider the Yoneda ring Y(e) := Ext_A~*(Se, Se) of e. We prove that if Y(e) is Artinian of finite global dimension, then A has finite global dimension if and only if so does Γ. We also investigate the situation where both A and Γ have finite global dimension. When A is Koszul and finite dimensional, this implies that Y(e) has finite global dimension. We end the paper with a reduction technique to compute the Cartan determinant of Artin algebras. We prove that if Y(e) has finite global dimension, then the Cartan determinants of A and Γ coincide. This provides a new way to approach the long-standing Cartan determinant conjecture.     

The spectrum for large sets of idempotent quasigroups

In this article we construct a large set of idempotent quasigroups of order 14. Combined with the results in Chang, JCMCC; and Teirlinck and Lindner, Eur J Combin 9 (1988), 83–89, this shows that the spectrum for large sets of idempotent quasigroups of order n [briefly, LIQ(n)] is the set all integers n≥ 3 with the exception of n=6. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 79–82, 2000     

Cohomology of the Vector Fields Lie Algebra and Modules of Differential Operators on a Smooth Manifold

Let M be a smooth manifold, the space of polynomial on fibers functions on T*M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M), of vector fields on M with coefficients in the space of linear differential operators on . This cohomology space is closely related to the Vect(M)-modules, (M), of linear differential operators on the space of tensor densities on M of degree .     

带可分解性质的幂等拟群大集

具有幂单正交侣的幂等拟群称为可分解的. 具有幂等正交侣的幂等拟群称为几乎可分解的. 若v 元集合上的所有分量互不相同的3-向量能够分拆成互不相交(幂等3-向量除外) 的v-2 个v 阶幂等拟群, 则称之为v 阶幂等拟群大集. 本文使用t-平衡设计(t=2; 3) 的方法给出了可分解幂等拟群大集、几乎可分解幂等拟群大集及可分解对称幂等拟群大集(即可分解高尔夫设计) 的构造方法, 给出了其存在性的若干结果.     

Densities of idempotent measures and large deviations

Considering measure theory in which the semifield of positive real numbers is replaced by an idempotent semiring leads to the notion of idempotent measure introduced by Maslov. Then, idempotent measures or integrals with density correspond to supremums of functions for the partial order relation induced by the idempotent structure. In this paper, we give conditions under which an idempotent measure has a density and show by many examples that they are often satisfied. These conditions depend on the lattice structure of the semiring and on the Boolean algebra in which the measure is defined. As an application, we obtain a necessary and sufficient condition for a family of probabilities to satisfy the large deviation principle.