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Year 2019, Volume: 26 Issue: 26, 29 - 40, 11.07.2019

Maryam Davoudian

https://doi.org/10.24330/ieja.586913

Abstract

References

  • T. Albu and P. F. Smith, Dual Krull dimension and duality, Rocky Mountain J. Math., 29 (1999), 1153-1165.
  • 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.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • L. Chambless, N-Dimension and N-critical modules, application to Artinian modules, Comm. Algebra, 8(16) (1980), 1561-1592.
  • M. Davoudian, Dimension of non- finitely generated submodules, Vietnam J. Math., 44 (2016), 817-827.
  • M. Davoudian, On alpha-quasi short modules, Int. Electron. J. Algebra, 21 (2017), 91-102.
  • M. Davoudian, Modules satisfying double chain condition on non nitely generated submodules have Krull dimension, Turkish J. Math., 41 (2017), 1570-1578.
  • M. Davoudian, Modules with chain condition on non- finitely generated submodules, Mediterr. J. Math., 15(1) (2018), Art. 1 (12 pp).
  • M. Davoudian, On alpha-semi-short modules, J. Algebr. Syst., 6 (2019), 91-99.
  • M. Davoudian, Dimension on non-essential submodules, J. Algebra Appl., 18(5) (2019), 1950089, DOI: 10.1142/S0219498819500890.
  • M. Davoudian and O. Ghayour, The lengths of Artinian modules with countable Noetherian dimensions, Bull. Iranian Math. Soc., 43(6) (2017), 1621-1628.
  • M. Davoudian, A. Halali and N. Shirali, On alpha-almost Artinian modules, Open Math., 14 (2016), 404-413.
  • M. Davoudian and O. A. S. Karamzadeh, Artinian serial modules over commutative (or, left Noetherian) rings are at most one step away from being Noetherian, Comm. Algebra, 44 (2016), 3907-3917.
  • M. Davoudian, O. A. S. Karamzadeh and N. Shirali, On alpha-short modules, Math. Scand., 114(1) (2014), 26-37.
  • M. Davoudian, O. A. S. Karamzadeh and N. Shirali, Erratum to On alpha-short modules, ResearchGate, researchgate.net/pro le/OAS Karamzadeh/research, June 2018, DOI: 10.13140/RG.2.2.36116.81280.
  • M. Davoudian and N. Shirali, On alpha-tall modules, Bull. Malays. Math. Sci. Soc., 41 (2018), 1739-1747.
  • R. Gordon and J. C. Robson, Krull Dimension, Memoirs of the American Mathematical Society, No. 133, American Mathematical Society, Providence, R.I., 1973.
  • J. Hashemi, O. A. S. Karamzadeh and N. Shirali, Rings over which the Krull dimension and Noetherian dimension of all modules coincide, Comm. Algebra, 37(2) (2009), 650-662.
  • J. Hein, Almost Artinian modules, Math. Scand., 45 (1979), 198-204.
  • O. A. S. Karamzadeh, Noetherian-Dimension, Ph.D. thesis, Exeter, 1974.
  • O. A. S. Karamzadeh and M. Motamedi, On alpha-DICC modules, Comm. Algebra, 22 (1994), 1933-1944.
  • O. A. S. Karamzadeh and M. Motamedi, Erratum to On alpha-DICC modules, Comm. Algebra, 22(6) (1994), 1933-1944, Comm. Algebra, 46 (2018), 2927.
  • O. A. S. Karamzadeh and A. R. Sajedinejad, Atomic modules, Comm. Algebra, 29(7) (2001), 2757-2773.
  • O. A. S. Karamzadeh and A. R. S. Nejad, On the Loewy length and the Noetherian dimension of Artinian modules, Comm. Algebra, 30 (2002), 1077-1084.
  • O. A. S. Karamzadeh and N. Shirali, On the countablity of Noetherian dimension of modules, Comm. Algebra, 32 (2004), 4073-4083.
  • G. Krause, Descending chains of submodules and the Krull-dimension of Noetherian modules, J. Pure Appl. Algebra, 3 (1973), 385-397.
  • B. Lemonnier, Deviation des ensembles et groupes abeliens totalement ordonnes, Bull. Sci. Math., 96 (1972), 289-303 (in French).
  • R. N. Roberts, Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math. Oxford Ser. (2), 26(103) (1975), 269-273.

ON α-ALMOST QUASI ARTINIAN MODULES

Year 2019, Volume: 26 Issue: 26, 29 - 40, 11.07.2019

Maryam Davoudian

https://doi.org/10.24330/ieja.586913

Abstract

In this article we introduce and study the concepts of \alpha-almost
quasi Artinian and \alpha-quasi Krull modules. Using these concepts we extend
some of the basic results of \alpha-almost Artinian and \alpha-Krull modules to \alpha-
almost quasi Artinian and \alpha-quasi Krull modules. We observe that if M is an
\alpha-quasi Krull module then the quasi Krull dimension of M is either \alpha or \alpha+1.

Keywords

Quasi Krull dimension quasi Noetherian dimension -Krull module -quasi Krull module -almost Noetherian module

References

  • T. Albu and P. F. Smith, Dual Krull dimension and duality, Rocky Mountain J. Math., 29 (1999), 1153-1165.
  • 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.
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • L. Chambless, N-Dimension and N-critical modules, application to Artinian modules, Comm. Algebra, 8(16) (1980), 1561-1592.
  • M. Davoudian, Dimension of non- finitely generated submodules, Vietnam J. Math., 44 (2016), 817-827.
  • M. Davoudian, On alpha-quasi short modules, Int. Electron. J. Algebra, 21 (2017), 91-102.
  • M. Davoudian, Modules satisfying double chain condition on non nitely generated submodules have Krull dimension, Turkish J. Math., 41 (2017), 1570-1578.
  • M. Davoudian, Modules with chain condition on non- finitely generated submodules, Mediterr. J. Math., 15(1) (2018), Art. 1 (12 pp).
  • M. Davoudian, On alpha-semi-short modules, J. Algebr. Syst., 6 (2019), 91-99.
  • M. Davoudian, Dimension on non-essential submodules, J. Algebra Appl., 18(5) (2019), 1950089, DOI: 10.1142/S0219498819500890.
  • M. Davoudian and O. Ghayour, The lengths of Artinian modules with countable Noetherian dimensions, Bull. Iranian Math. Soc., 43(6) (2017), 1621-1628.
  • M. Davoudian, A. Halali and N. Shirali, On alpha-almost Artinian modules, Open Math., 14 (2016), 404-413.
  • M. Davoudian and O. A. S. Karamzadeh, Artinian serial modules over commutative (or, left Noetherian) rings are at most one step away from being Noetherian, Comm. Algebra, 44 (2016), 3907-3917.
  • M. Davoudian, O. A. S. Karamzadeh and N. Shirali, On alpha-short modules, Math. Scand., 114(1) (2014), 26-37.
  • M. Davoudian, O. A. S. Karamzadeh and N. Shirali, Erratum to On alpha-short modules, ResearchGate, researchgate.net/pro le/OAS Karamzadeh/research, June 2018, DOI: 10.13140/RG.2.2.36116.81280.
  • M. Davoudian and N. Shirali, On alpha-tall modules, Bull. Malays. Math. Sci. Soc., 41 (2018), 1739-1747.
  • R. Gordon and J. C. Robson, Krull Dimension, Memoirs of the American Mathematical Society, No. 133, American Mathematical Society, Providence, R.I., 1973.
  • J. Hashemi, O. A. S. Karamzadeh and N. Shirali, Rings over which the Krull dimension and Noetherian dimension of all modules coincide, Comm. Algebra, 37(2) (2009), 650-662.
  • J. Hein, Almost Artinian modules, Math. Scand., 45 (1979), 198-204.
  • O. A. S. Karamzadeh, Noetherian-Dimension, Ph.D. thesis, Exeter, 1974.
  • O. A. S. Karamzadeh and M. Motamedi, On alpha-DICC modules, Comm. Algebra, 22 (1994), 1933-1944.
  • O. A. S. Karamzadeh and M. Motamedi, Erratum to On alpha-DICC modules, Comm. Algebra, 22(6) (1994), 1933-1944, Comm. Algebra, 46 (2018), 2927.
  • O. A. S. Karamzadeh and A. R. Sajedinejad, Atomic modules, Comm. Algebra, 29(7) (2001), 2757-2773.
  • O. A. S. Karamzadeh and A. R. S. Nejad, On the Loewy length and the Noetherian dimension of Artinian modules, Comm. Algebra, 30 (2002), 1077-1084.
  • O. A. S. Karamzadeh and N. Shirali, On the countablity of Noetherian dimension of modules, Comm. Algebra, 32 (2004), 4073-4083.
  • G. Krause, Descending chains of submodules and the Krull-dimension of Noetherian modules, J. Pure Appl. Algebra, 3 (1973), 385-397.
  • B. Lemonnier, Deviation des ensembles et groupes abeliens totalement ordonnes, Bull. Sci. Math., 96 (1972), 289-303 (in French).
  • R. N. Roberts, Krull dimension for Artinian modules over quasi local commutative rings, Quart. J. Math. Oxford Ser. (2), 26(103) (1975), 269-273.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Maryam Davoudian This is me

Publication Date July 11, 2019
Published in Issue Year 2019 Volume: 26 Issue: 26

Cite

APA Davoudian, M. (2019). ON α-ALMOST QUASI ARTINIAN MODULES. International Electronic Journal of Algebra, 26(26), 29-40. https://doi.org/10.24330/ieja.586913
AMA Davoudian M. ON α-ALMOST QUASI ARTINIAN MODULES. IEJA. July 2019;26(26):29-40. doi:10.24330/ieja.586913
Chicago Davoudian, Maryam. “ON α-ALMOST QUASI ARTINIAN MODULES”. International Electronic Journal of Algebra 26, no. 26 (July 2019): 29-40. https://doi.org/10.24330/ieja.586913.
EndNote Davoudian M (July 1, 2019) ON α-ALMOST QUASI ARTINIAN MODULES. International Electronic Journal of Algebra 26 26 29–40.
IEEE M. Davoudian, “ON α-ALMOST QUASI ARTINIAN MODULES”, IEJA, vol. 26, no. 26, pp. 29–40, 2019, doi: 10.24330/ieja.586913.
ISNAD Davoudian, Maryam. “ON α-ALMOST QUASI ARTINIAN MODULES”. International Electronic Journal of Algebra 26/26 (July 2019), 29-40. https://doi.org/10.24330/ieja.586913.
JAMA Davoudian M. ON α-ALMOST QUASI ARTINIAN MODULES. IEJA. 2019;26:29–40.
MLA Davoudian, Maryam. “ON α-ALMOST QUASI ARTINIAN MODULES”. International Electronic Journal of Algebra, vol. 26, no. 26, 2019, pp. 29-40, doi:10.24330/ieja.586913.
Vancouver Davoudian M. ON α-ALMOST QUASI ARTINIAN MODULES. IEJA. 2019;26(26):29-40.