An algebraic derivation of a certain exact sequence

ALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)

We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.

ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

An Algebraic Characterization of Certain Orthonormal Systems1

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

An Exact Sequence for Submersions

As our second example we consider the case where TT is a differentiable submersion (in the usual sense) of codimension 1. Thus we assume that X, B are C°°-manifolds of dimensions n + 1 and n, respectively, and that TT is a regular differentiate map. Such a submersion is orientable if the induced line element field on X is orientable, and w will be called simple if w~(b) is connected for all bÇEB.