AFRICA MATHEMATICS ANNALS

Quasi-graduations of Rings and Modules, Criteria of Generalized Analytic Independence

Youssouf M. DIAGANA
UFR-SFA Laboratoire de Mathématiques et Informatique
Université d'Abobo-Adjamé, 02 BP 801 Abidjan 02, CÔTE D'IVOIRE

AMS Classifications: 13A02, 13A30, 13D40, 13H15 .
Key words : filtrations, quasi-graduations of rings and modules, Generalized analytic independence.

Abstract:

A +quasi-graduation of a commutative ring is a family of subgroups of such that is a subring of ; and ; for all . We will show that elements of are -independent of order with respect to a +quasi-graduation if and only if the two properties which follow hold: they are -independent of order and there exists a relation of compatibility between and where is the -submodule of generated by these elements. The concept of -independence will be extended to modules and we give criteria of -independence in terms of isomorphisms of graded modules .