Quasi-bigraduations of Modules, criteria of generalized analytic independence

Diagana, Y. M.

doi:10.22124/jart.2018.11137.1113

Quasi-bigraduations of Modules, criteria of generalized analytic independence

Document Type : Research Paper

Author

Y. M. Diagana

Laboratoire Math $a c u t e e$ matiques-Informatique, Universit $a c u t e e$ Nangui Abrogoua, Abidjan, C $h a t o$ te d'Ivoire

10.22124/jart.2018.11137.1113

Abstract

Let

R

be a ring. For a quasi-bigraduation

f = I_{(p, q)}

R

\ we define an

f^{+} -

quasi-bigraduation of an

R

-module

M

\ by a family

g = (G_{(m, n)})_{(m, n) \in (Z \times Z) \cup {\infty}}

of subgroups of

M

such that

G_{\infty} = (0)

and

I_{(p, q)} G_{(r, s)} \subseteq G_{(p + r, q + s)},

for all

(p, q)

and all

(r, s) \in (N \times N) \cup {\infty} .

Here we show that

r

elements of

R

are

J -

independent of
order

k

with respect to the

f^{+}

quasi-bigraduation

g

if and only if
the following two properties hold: they are

J -

independent of order

k

with respect to the

^{+}

%
quasi-bigraduation of ring

f_{2} (I_{(0, 0)}, I)

and there exists a relation of
compatibility between

g

and

g_{I}

, where

I

is the sub-

A -

%
module of

R

constructed by these elements. We also show that criteria of

J -

independence of compatible
quasi-bigraduations of module are given in terms of isomorphisms of graded
algebras.

Keywords

Quasi-bigraduations of Modules, criteria of generalized analytic independence

Volume 6, Issue 2
December 2018
Pages 79-96

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Quasi-bigraduations of Modules, criteria of generalized analytic independence

Volume 6, Issue 2December 2018Pages 79-96

Files

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How to cite

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Volume 6, Issue 2
December 2018
Pages 79-96