Coincidence Points and Invariant Approximation Results for Multimaps

Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.     

Wightman axiomatic approach in noncommutative field theory

The axiomatic approach based on Wightman functions is developed in noncommutative field theory. We prove that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 403#x2013;416, February, 2005.     

CERTAIN COMMUTATIVITY CONDITIONS FOR RINGS WITH UNITY

ＣＥＲＴＡＩＮＣＯＭＭＵＴＡＴＩＶＩＴＹＣＯＮＤＩＴＩＯＮＳＦＯＲＲＩＮＧＳＷＩＴＨＵＮＩＴＹＶ．Ｗ．Ｊａｃｏｂ，Ｍ．ＡｓｈｒａｆａｎｄＭ．Ａ．Ｑｕａｄｒｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＡｌｉｇａｒｈＭｕｓｌｉｍＵｎｉｖｅｒｓｉｔ...     

Coincidence and fixed points for hybrid strict contractions

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T-weak commutativity for a hybrid pair (f,T) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.     

Commutativity Conditions for Rings and Generalized 2-CN Rings

Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.     

Nonlinear Strong Commutativity Preserving Maps on Prime Rings

Let 𝒜 be a unital prime ring containing a nontrivial idempotent P. Assume that Φ: 𝒜 → 𝒜 is a nonlinear surjective map. It is shown that Φ preserves strong commutativity if and only if Φ has the form Φ(A) = αA + f(A) for all A ∈ 𝒜, where α ∈ {1, ?1} and f is a map from 𝒜 into 𝒵(𝒜). As an application, a characterization of nonlinear surjective strong commutativity preserving maps on factor von Neumann algebras is obtained.     

Universal homogeneous derivations of graded ϵ-commutative algebras

Let K be a commutative ring, let ? be an abelian group, and let ?:?x?→K be a commutation factor over ?.A ? graded K-algebra is said to be ?-commutative if its ?-bracket is identically zero, (K,?) derivations from a given ?-commutative ?-graded K-algebra A into bimodules are studied. It is proved that for each λ?? there exists a universal initial (k,?)-derivation of degree λ of A. For each λ?? a natural module of (K, ?, λ)-differentials of A along with a differential map is constructed. It is proved that each derivation of A canonically equipps this module with a structure of differential module. Applications and examples are given. It is shown that the first order exterior differentials which are known from the theory of smooth graded manifolds are universal initial homogeneous derivations of the sort considered hereby.     

On strong reality of the unipotent Lie-type subgroups over a field of characteristic 2

A group G is called strongly real if its every nonidentity element is strongly real, i.e. conjugate with its inverse by an involution of G. We address the classical Lie-type groups of rank l, with l ≤ 4 and l ≤ 13, over an arbitrary field, and the exceptional Lie-type groups over a field K with an element η such that the polynomial X ² + X + η is irreducible either in K[X] or K ₀[X] (in particular, if K is a finite field). The following question is answered for the groups under study: What unipotent subgroups of the Lie-type groups over a field of characteristic 2 are strongly real?     

有正则元的环的若干交换性条件

推广了Moharram A.Khan,Jeddah的结论,得到了有正则元的环的几个交换性条件.     

Probabilistic aspects of ZM-groups

In this paper we study probabilistic aspects such as the (cyclic) subgroup commutativity degree and different types of factorization numbers of ZM-groups. We show that these quantities can be computed using the sizes of the conjugacy classes of these groups. In the end, we point out a class of groups whose (cyclic) subgroup commutativity degree vanishes asymptotically.