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Prime extension dimension of a module | ||
| Journal of Algebra and Related Topics | ||
| مقاله 6، دوره 6، شماره 2، اسفند 2018، صفحه 97-106 اصل مقاله (302.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2018.11232.1116 | ||
| نویسندگان | ||
| T. Duraivel1؛ S. Mangayarcarassy2؛ K. Premkumar* 3 | ||
| 1Department of Mathematics, Pondicherry University, Puducherry, India. | ||
| 2Department of Mathematics, Pondicherry Engineering College, Puducherry, India. | ||
| 3Department of Mathematics, Indira Gandhi Institute of Technology, Odisha, India. | ||
| چکیده | ||
| We have that for a finitely generated module $M$ over a Noetherian ring $A$ any two RPE filtrations of $M$ have same length. We call this length as prime extension dimension of $M$ and denote it as $\mr{pe.d}_A(M)$. This dimension measures how far a module is from torsion freeness. We show for every submodule \(N\) of \(M\), \(\mr{pe.d}_A(N)\leq\mr{pe.d}_A(M)\) and \(\mr{pe.d}_A(N)+\mr{pe.d}_A(M/N)\geq\mr{pe.d}_A(M)\). We compute the prime extension dimension of a module using the prime extension dimensions of its primary submodules which occurs in a minimal primary decomposition of \(0\) in \(M\). | ||
| کلیدواژه‌ها | ||
| Prime submodules؛ Primary decomposition؛ Prime filtration and Regular prime extension filtration | ||
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