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Quasi-bigraduations of Modules, criteria of generalized analytic independence | ||
| Journal of Algebra and Related Topics | ||
| مقاله 5، دوره 6، شماره 2، اسفند 2018، صفحه 79-96 اصل مقاله (394.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2018.11137.1113 | ||
| نویسنده | ||
| Y. M. Diagana* | ||
| Laboratoire Math$acute{e}$matiques-Informatique, Universit$acute{e}$ Nangui Abrogoua, Abidjan, C$hat{o}$te d'Ivoire | ||
| چکیده | ||
| Let $\mathcal{R}$ be a ring. For a quasi-bigraduation $f=I_{(p,q)}$ of ${\mathcal{R}} $ \ we define an $f^{+}-$quasi-bigraduation of an ${% \mathcal{R}}$-module ${\mathcal{M}}$ \ by a family $g=(G_{(m,n)})_{(m,n)\in \left(\mathbb{Z}\times \mathbb{Z}\right) \cup \{\infty \}}$ of subgroups of $% {\mathcal{M}}$ such that $G_{\infty }=(0) $ and $I_{(p,q)}G_{(r,s)}\subseteq G_{(p+r,q+s)},$ for all $(p,q)$ and all $(r,s)\in \left(\mathbb{N} \times \mathbb{N}\right) \cup \{\infty \}.$ Here we show that $r$ elements of ${\mathcal{R}}$ 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-$\mathcal{A}-$% module of $\mathcal{R}$ 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. | ||
| کلیدواژه‌ها | ||
| Quasi-bigraduations؛ modules؛ generalized analytic independence | ||
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