AFRICA MATHEMATICS ANNALS

Independence on Quasi-Bigraduations
of Rings and Analytic Spread

Eugène Deval Béché, Youssouf M. DIAGANA
and Pierre K. BROU
Université Nangui Abrogoua, UFR-SFA
Laboratoire Mathématiques-Informatique
02 BP 801 Abidjan 02 Abidjan, Côte d'Ivoire

Mathematics Subject Classification: (2010) 13A02, 13A15, 13A30, 13B25, 13F20
Key words: Quasi-bigraduations, analytic spread

Abstract:

When f = _∈∪{∞} is a ⁺quasi-bigraduation on a ring , an f⁺-quasi-bigraduation of an -module is a family  g = (G_(m,n)) of subgroups of such that G_∞ = (0) and I_(m,n)G_(p,q) ⊆ G_(m+p,n+q), for all (m,n) and (p,q) ∈ ∪{∞}.

We give comparisons of several extensions of analytic spread for compatible ⁺quasi-bigraduations on a ring in term of generalized independences.