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$\tau_w$-Loewy modules and their applications

김환구|임정욱|De Chuan Zhou
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1617-1642|DOI 10.4134/BKMS.b190049

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키워드

$w$-operation$w$-Artiniam module$w$-Loewy module$w$-simple module
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초록

In this paper, we study a theory for the structure of $\tau_w$-Loewy series of modules over commutative rings, where $\tau_w$ is the hereditary torsion theory induced by the so-called $w$-operation, and explore the relationship between $\tau_w$-Loewy modules and $w$-Artinian modules.

Abstract

In this paper, we study a theory for the structure of $\tau_w$-Loewy series of modules over commutative rings, where $\tau_w$ is the hereditary torsion theory induced by the so-called $w$-operation, and explore the relationship between $\tau_w$-Loewy modules and $w$-Artinian modules.

참고문헌 (15)

  1. P. E. Bland, "Topics in Torsion Theory" (1998), Wiley-VCH Verlag Berlin GmbH
  2. José L. Bueso, "Semiartinian modules relative to a torsion theory", Communications in Algebra, 13(3), pp.631~644 (2007), Informa UK Limited[DOI]
  3. Alberto Facchini, "Loewy and Artinian modules over commutative rings", Annali di Matematica Pura ed Applicata, 128(1), pp.359~374 (1981), Springer Science and Business Media LLC[DOI]
  4. Sarah Glaz, "Flat ideals II", Manuscripta Mathematica, 22(4), pp.325~341 (1977), Springer Science and Business Media LLC[DOI]
  5. Wolfgang Krull, "Zur Theorie der allgemeinen Zahlringe", Mathematische Annalen, 99(1), pp.51~70 (1928), Springer Science and Business Media LLC[DOI]
  6. D. G. Northcott, "An Introduction to Homological Algebra" (1960), Cambridge University Press
  7. undefined, "The structure of Loewy modules.", Journal für die reine und angewandte Mathematik (Crelles Journal), 1972(254), pp.204~220 (1972), Walter de Gruyter GmbH[DOI]
  8. undefined, "Loewy series of modules.", Journal für die reine und angewandte Mathematik (Crelles Journal), 1974(265), pp.183~200 (1974), Walter de Gruyter GmbH[DOI]
  9. F. G. Wang, "Finitely presented type modules and w-coherent rings", J. Sichuan Normal Univ. (Nat. Sci.), 33, pp.1~9 (2010)
  10. F. G. Wang, "Foundations of Commutative Rings and Their Modules" (2016), Springer
  11. Wang Fanggui, "On w-modules over strong mori domains", Communications in Algebra, 25(4), pp.1285~1306 (2007), Informa UK Limited[DOI]
  12. Huayu Yin, "ω-MODULES OVER COMMUTATIVE RINGS", 대한수학회지, 48(1), pp.207~222 (2011), 대한수학회
  13. J. Zhang, "The Krull-Remak-Schmidt theorem on several classes of w-modules", J. Sichuan Normal Univ. (Nat. Sci.), 34, pp.601~604 (2011)
  14. J. Zhang, "The w-socles of w-modules", J. Sichuan Normal Univ. (Nat. Sci.), 36, pp.807~810 (2013)
  15. S. Q. Zhao, "Flat modules over a commutative ring are w-modules", J. Sichuan Normal Univ. (Nat. Sci.), 35, pp.364~366 (2012)

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