Volume 5, Issue 4

We first establish the commutativity for the semiprime ring satisfying [ x n , y ] x r = ± y s [ x, y m ] y t for all x, y in R , where m, n, r, s and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s -unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s -unital.

The author considers a special kind of B -product which is called the multiplicative B -product. The most important property of multiplicative B -product is that it preserves multiplicativity of functions.

General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established.

A universal C *-algebra is constructed which is generated by a partial isometry. Using grading on this algebra we construct an analog of Cuntz algebras which gives a homotopical interpretation of KK -groups. It is proved that this algebra is homotopy equivalent up to stabilization by 2×2 matrices to M 2 ( C ). Therefore those algebras are KK -isomorphic.

The correct formulation of a characteristic problem and a Darboux type problem in the special weighted functional spaces for an ultrahyperbolic equation is investigated.

The object of the present paper is to show the properties of the Salagean operator for analytic functions in the open unit disk. The main results obtained here extend and improve the earlier results obtained by several authors.

Formulas for calculating the sum of singular series corresponding to the number of representations of integers by some quadratic forms in 12 variables with integral coefficient are derived.

The boundary properties of second-order partial derivatives of the Poisson integral are studied for a half-space .