BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2000 | Volume:26 | Issue:1|Papers Count:8

Let D be a division ring with center F and denote by [D,D] the group generated additively by the additive commentators in D. In zero characteristic, we characterize subdivision rings and subfields of D in terms of some subgroups of [D,D]. In particular we show that there is a bijection between maximal subfields of D and maximal subgroups of [D,D].

The nonlinear generalized conjugated gradient (NGCG) methods are iterative methods for solving nonlinear systems [3]. Applying the preconditioner's idea to these methods is caused that variant of iterative methods produce. Since, solving the Wiener-Hopf-like nonlinear boundary integral equations (WNBIE) is very hard, it is interesting to extend the decried methods to this class of equations. Therefore, two new preconditioners are given for this class of the WN-BIE.

Let A be a unital complex Banach algebra and D be a derivation on A. LetK={x ε rad (A): for every natural number n, Dnx ε rad (A)}. Then D preserves the primitive ideals of A invariant if and only if K is closed. We also prove that D maps into the radical if the induced derivation Dk:A/K->A/K is centralising, or K is closed and Dk is spectrally bounded. We also prove some related results.

Let T=[AMNB] be the ring of a Morita context.  The main results proved in this paper are:(i) If MA and NB are finitely generated and A and Bare metrically right repetitive; then so is T.(ii) If either MA and NB ate finitely generated or BM and AN are finitely generated and A and Bare metrically strongly  p-regular, then so is T.

Let A be a function algebra and T be a homomorphism from A into Lip a (K), (0 < a £ 1) or from Lip a (K) into A. We investigate the compactness of T and give necessary and sufficient conditions under which a homomorphism from an analytic function algebra into a function algebra A is compact. Also this note gives necessary and sufficient conditions under which every homomorphism from a natural Banach algebra into function algebra is compact.

We extend the notions of right (and left) distal functions defined on a semigroup, and define them on a topological space under the action of a semigroup, and study their properties. We then characterize (in terms of these function spaces) the universal right topological, left topological, and topological transformation group compactifications of a semitopological transformation semigroup.

In this note, we study infinite groups satisfying the condition E2(¥) i.e. groups in which every infinite subset contains two distinct elements x, y such that [x, y, y] = 1.