ON α -QUASI SHORT MODULES

Year 2017, , 91 - 102, 17.01.2017

Maryam Davoudian

https://doi.org/10.24330/ieja.296105

Cited By: 1

Abstract

We introduce and study the concept of α-quasi short modules.

Keywords

α -short module, α -almost Noetherian module, α -quasi short module

References

• [1] T. Albu and S. T. Rizvi,Chain conditions on quotient finite dimensional modules
• , Comm. Algebra, 29(5) (2001), 1909-1928.
• [2] T. Albu and P. F. Smith,Dual Krull dimension and duality, Rocky Mountain
• J. Math., 29(4) (1999), 1153-1165.
• [3] T. Albu and P. Vamos,Global Krull dimension and global dual Krull dimension of valuation rings
• , Abelian groups, module theory, and topology (Padua, 1997),
• Lecture Notes in Pure and Appl. Math., 201, Dekker, New York, (1998), 37-54.
• [4] G. Bilhan and P. F. Smith, Short modules and almost Noetherian modules,
• Math. Scand., 98(1) (2006), 12-18.
• [5] L. Chambless, N-Dimension and N-critical modules, application to Artinian
• modules, Comm. Algebra, 8(16) (1980), 1561-1592.
• [6] M. Davoudian, Dimension of non-finitely generated submodules, Vietnam J. Math., 44(4) (2016), 817-827.
• [7] M. Davoudian and O. A. S. Karamzadeh, Artinian serial modules over com-
• mutative (or, left Noetherian) rings are at most one step away from being
• Noetherian, Comm. Algebra, 44(9) (2016), 3907-3917.
• [8] M. Davoudian, O. A. S. Karamzadeh and N. Shirali, On α-short modules,
• Math. Scand., 114(1) (2014), 26-37.
• [9] R. Gordon, Gabriel and Krull dimension, Ring theory (Proc. Conf., Univ.
• Oklahoma, Norman, Okla., 1973), 241-295, Lecture Notes in Pure and Appl. Math., 7, Dekker, New York, 1974.