Extremal generalized centralizers in matrix algebras

We describe matrices with extremal generalized centralizers over algebraically closed fields.     

Some commutativity criteria for prime rings with differential identities on Jordan ideals

In this article, we present some commutativity theorems for a ring R equipped with a generalized derivation satisfying certain differential identities on Jordan ideals of R. Some related results for prime rings are also discussed. Finally; we provide examples to show that the assumed restrictions are not superfluous.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.     

A Generalization of Commutativity Degree of Finite Groups

The commutativity degree of a finite group is the probability that two arbitrarily chosen group elements commute. This notion has been generalized in a number of ways. The object of this article is to study yet another generalization of the same notion, which further extends some of the existing generalizations.     

Spectral Representation of Analytic Diagonalizable Matrix-valued Functions that Commute with their Derivative

In 1981, Goff showed that an analytic n × n self-adjoint matrix-valued function A defined on an open interval I of the real axis that commutes with its derivative must be functionally commutative. We generalize Goff's result by showing that it remains valid for diagonalizable matrices and that we need only require this diagonalizability property on an open subinterval I o of I . We also show that diagonalizability property propagates from the subinterval I o to the whole interval I and we obtain the spectral representation of the function A and its derivatives D j A , j = 0,1,2, < .     

Characterization of supercommuting matrices

For a given n–by–n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Two Theorems on the Commutativity of Arbitrary Rings

We prove a theorem on the commutativity of the PI ring and use it to generalize a famous theorem of Herstein.     

Weak order stochastic Runge–Kutta methods for commutative stochastic differential equations

A new explicit stochastic Runge–Kutta scheme of weak order 2 is proposed under a commutativity condition, which is derivative-free and which attains order 4 for ordinary differential equations. The weak order conditions are derived by utilizing multi-colored rooted tree analysis and a solution is found in a transparent way. The scheme is compared with other derivative-free and weak second order schemes in numerical experiments.