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A note on $\phi$-Pr\"{u}fer $v$-multiplication rings

Xiaolei Zhang
대한수학회 (The Korean Mathematical Society)|2022.09|대한수학회보 (Bulletin of the KMS)|제59권 제5호|pp. 1289-1304|DOI 10.4134/BKMS.b210754

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키워드

$\phi$-$\PvMR$$\phi$-$w$-flat modulenonnil-absolutely $w$-pure module$w$-projective module
주제분류수학

초록

In this note, we show that a strongly $\phi$-ring $R$ is a $\phi$-$\PvMR$ if and only if any $\phi$-torsion-free $R$-module is $\phi$-$w$-flat, if and only if any $\GV$-torsion-free divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any $\GV$-torsion-free $h$-divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any finitely generated nonnil ideal of $R$ is $w$-projective.

Abstract

In this note, we show that a strongly $\phi$-ring $R$ is a $\phi$-$\PvMR$ if and only if any $\phi$-torsion-free $R$-module is $\phi$-$w$-flat, if and only if any $\GV$-torsion-free divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any $\GV$-torsion-free $h$-divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any finitely generated nonnil ideal of $R$ is $w$-projective.

참고문헌 (24)

  1. D. F. Anderson, "On φ-Prufer rings and φ-Bezout rings", Houston J. Math, 30(2), pp.331~343 (2004)
  2. D. F. Anderson, "On φ-Dedekind rings and φ-Krull rings", Houston J. Math, 31(4), pp.1007~1022 (2005)
  3. A. Badawi, "On φ-chained rings and φ-pseudo-valuation rings", Houston J. Math, 27(4), pp.725~736 (2001)
  4. A. Badawi, "On nonnil-Noetherian rings", Comm. Algebra, 31(4), pp.1669~1677 (2003)[DOI]
  5. E. E. Enochs, "Relative homological algebra", De Gruyter Expositions in Mathematics, 30 (2000), Walter de Gruyter & Co[DOI]
  6. W. Fanggui, "On strong Mori domains", J. Pure Appl. Algebra, 135(2), pp.155~165 (1999)[DOI]
  7. László Fuchs, "Modules over Non-Noetherian Domains", Mathematical Surveys and Monographs (2000), American Mathematical Society[DOI]
  8. Sarah Glaz, "Commutative Coherent Rings", Lecture Notes in Mathematics (1989), Springer Berlin Heidelberg[DOI]
  9. J. A. Huckaba, "Commutative rings with zero divisors", Monographs and Textbooks in Pure and Applied Mathematics, 117 (1988), Marcel Dekker, Inc
  10. B. Khoualdia, "Nonnil-coherent rings", Beitr. Algebra Geom, 57(2), pp.297~305 (2016)[DOI]
  11. H. Kim, "On φ-strong Mori rings", Houston J. Math, 38(2), pp.359~371 (2012)
  12. W. V. Vasconcelos, "On finitely generated flat modules", Trans. Amer. Math. Soc, 138, pp.505~512 (1969)[DOI]
  13. Fanggui Wang, "w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS", 대한수학회지, 51(3), pp.509~525 (2014), 대한수학회
  14. F. Wang, "Two generalizations of projective modules and their applications", J. Pure Appl. Algebra, 219(6), pp.2099~2123 (2015)[DOI]
  15. Fanggui Wang, "Foundations of Commutative Rings and Their Modules", Algebra and Applications (2016), Springer Singapore[DOI]
  16. Fanggui Wang, "Relative FP-injective modules and relative IF rings", Communications in Algebra, 49(8), pp.3552~3582 (2021), Informa UK Limited[DOI]
  17. Fanggui Wang, "THE ω-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS", 대한수학회보, 52(4), pp.1327~1338 (2015), 대한수학회
  18. Shiqi Xing, "Purity over Prüfer v-multiplication domains", Journal of Algebra and Its Applications, 17(06), pp.1850100~ (2018), World Scientific Pub Co Pte Lt[DOI]
  19. Shiqi Xing, "Purity over Prüfer v-multiplication domains, II", Journal of Algebra and Its Applications, 17(12), pp.1850223~ (2018), World Scientific Pub Co Pte Lt[DOI]
  20. "Some remarks on φ-Dedekind rings and φ-Prufer rings"[URL]
  21. X. Zhang, "On characterizations of w-coherent rings II", Comm. Algebra, 49(9), pp.3926~3940 (2021)[DOI]
  22. Xiaolei Zhang, "ON 𝜙-w-FLAT MODULES AND THEIR HOMOLOGICAL DIMENSIONS", 대한수학회보, 58(4), pp.1039~1052 (2021), 대한수학회[DOI]
  23. Wei Zhao, "On $\Phi$-flat modules and $\Phi$-Pr\"{u}fer rings", 대한수학회지, 55(5), pp.1221~1233 (2018), 대한수학회
  24. Wei Zhao, "On ø-von Neumann regular rings", 대한수학회지, 50(1), pp.219~229 (2013), 대한수학회

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