λ³Έλ¬Έ λ°”λ‘œκ°€κΈ°
KERD
λ…Όλ¬ΈKCI λ“±μž¬

ON πœ™-EXACT SEQUENCES AND πœ™-PROJECTIVE MODULES

Wei Zhao
λŒ€ν•œμˆ˜ν•™νšŒ (The Korean Mathematical Society)|2021.11|λŒ€ν•œμˆ˜ν•™νšŒμ§€ (Journal of the KMS)|제58ꢌ 제6호|pp. 1513-1528|DOI 10.4134/JKMS.j210180

2

쑰회

0

λ‹€μš΄λ‘œλ“œ

3

인용

0

μ°Έκ³ λ¬Έν—Œ

ν‚€μ›Œλ“œ

Ο•-exact sequencenonnil-divisible moduleΟ•-projective module
μ£Όμ œλΆ„λ₯˜μˆ˜ν•™

초둝

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map πœ™ : R β†’ RNil(R) by Ο• ( r ) = r 1 for r ∈ R and πœ“ : M β†’ MNil(R) by ψ ( x ) = x 1 for x ∈ M. Then πœ“(M) is a πœ™(R)-module. An R-module P is said to be πœ™-projective if πœ“(P) is projective as a πœ™(R)-module. In this paper, πœ™-exact sequences and πœ™-projective R-modules are introduced and the rings over which all R-modules are πœ™-projective are investigated.

Abstract

Let R be a commutative ring with prime nilradical Nil(R) and M an R-module. Define the map πœ™ : R β†’ RNil(R) by Ο• ( r ) = r 1 for r ∈ R and πœ“ : M β†’ MNil(R) by ψ ( x ) = x 1 for x ∈ M. Then πœ“(M) is a πœ™(R)-module. An R-module P is said to be πœ™-projective if πœ“(P) is projective as a πœ™(R)-module. In this paper, πœ™-exact sequences and πœ™-projective R-modules are introduced and the rings over which all R-modules are πœ™-projective are investigated.

μ°Έκ³ λ¬Έν—Œ (28)

  1. D. F. Anderson, "On Ξ¦-Prufer rings and Ξ¦-Bezout rings", Houston J. Math, 30(2), pp.331~343 (2004)
  2. D. F. Anderson, "Ξ¦-Dedekind rings and Ξ¦-Krull rings", Houston J. Math, 31(4), pp.1007~1022 (2005)
  3. K. Bacem, "Nonnil-coherent rings", Beitr. Algebra Geom, 57(2), pp.297~305 (2016)
  4. A. Badawi, "Advances in commutative ring theory", pp.101~110 (1997), Dekker
  5. A. Badawi, "On Ξ¦-pseudo-valuation rings. II", Houston J. Math, 26(3), pp.473~480 (2000)
  6. A. Badawi, "On Ξ¦g-chained rings and Ξ¦-pseudo-valuation rings", Houston J. Math, 27(4), pp.4~725 (2001)
  7. A. Badawi, "On divided rings and Ξ¦-pseudo-valuation rings, Commutative rings", pp.5~14 (2002), Nova Sci. Publ
  8. Ayman Badawi, "On Nonnil-Noetherian Rings", Communications in Algebra, 31(4), pp.1669~1677 (2003), Informa UK Limited[DOI]
  9. Ayman Badawi, "Factoring Nonnil Ideals into Prime and Invertible Ideals", Bulletin of the London Mathematical Society, 37(5), pp.665~672 (2005), Wiley[DOI]
  10. A. Badawi, "Commutative algebra and its applications", pp.21~40 (2009), Walter de Gruyter
  11. A. Badawi, "Strong ring extensions and Ξ¦-pseudo-valuation rings", Hous-ton J. Math, 32(2), pp.379~398 (2006)
  12. A. Badawi, "Some finiteness conditions on the set of overrings of a Ξ¦-ring", Houston J. Math, 34(2), pp.397~408 (2008)
  13. A. Badawi, "Arithmetical properties of commutative rings and monoids", pp.2005, Chapman & Hall
  14. A. Badawi, "On Ξ¦-Mori rings", Houston J. Math, 32(1), pp.1~32 (2006)
  15. Ali Benhissi, "Nonnil-Noetherian Rings and Formal Power Series", Algebra Colloquium, 27(03), pp.361~368 (2020), World Scientific Pub Co Pte Ltd[DOI]
  16. Ahmad Yousefian Darani, "On $\phi$-Schreier rings", λŒ€ν•œμˆ˜ν•™νšŒμ§€, 53(5), pp.1057~1075 (2016), λŒ€ν•œμˆ˜ν•™νšŒ
  17. Rachida El Khalfaoui, "The Ο•-Krull dimension of some commutative extensions", Communications in Algebra, 48(9), pp.3800~3810 (2020), Informa UK Limited[DOI]
  18. Abdelhaq El Khalfi, "On Ο•-piecewise Noetherian rings", Communications in Algebra, 49(3), pp.1324~1337 (2021), Informa UK Limited[DOI]
  19. Sana Hizem, "Nonnil-Noetherian rings and the SFT property", Rocky Mountain Journal of Mathematics, 41(5), pp.1483~1500 (2011), Rocky Mountain Mathematics Consortium[DOI]
  20. H. Kim, "On Ξ¦-strong Mori rings", Houston J. Math, 38(2), pp.359~371 (2012)
  21. C. Lomp, "Groups, rings and group rings", pp.205~217 (2009), Amer. Math. Soc
  22. Ingegerd PalmΓ©r, "Explicit formulae for the global homological dimensions of trivial extensions of rings", Journal of Algebra, 27(2), pp.380~413 (1973), Elsevier BV[DOI]
  23. F. Wang, "Foundations of commutative rings and their modules" (2016), Springer
  24. X. Y. Yang, "On nonnil-Noetherian rings", Southeast Asian Bull. Math, 33(6), pp.1215~1223 (2009)
  25. W. Zhao, "A few kinds of commutative rings with the nilradical as prime ideal", J. Neijiang Normal University, 30(6875), pp.11~14 (2015)
  26. Wei Zhao, "On $\Phi$-flat modules and $\Phi$-Pr\"{u}fer rings", λŒ€ν•œμˆ˜ν•™νšŒμ§€, 55(5), pp.1221~1233 (2018), λŒ€ν•œμˆ˜ν•™νšŒ
  27. Wei Zhao, "On ΓΈ-von Neumann regular rings", λŒ€ν•œμˆ˜ν•™νšŒμ§€, 50(1), pp.219~229 (2013), λŒ€ν•œμˆ˜ν•™νšŒ
  28. Wei Zhao, "On Ξ¦-projective modules and Ξ¦-PrΓΌfer rings", Communications in Algebra, 48(7), pp.3079~3090 (2020), Informa UK Limited[DOI]

κ΄€λ ¨ λ…Όλ¬ΈAIμΆ”μ²œ

On $\Phi$-flat modules and $\Phi$-Pr\"{u}fer ringsWei ZhaoλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒμ§€2018 Β· 제55ꢌ 제5호Nonnil-P-coherent rings and nonnil-PP-ringsκΉ€ν™˜κ΅¬, El Houssaine Oubouhou, Najib MahdouλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒλ³΄2024 Β· 제61ꢌ 제5호On prime submodules of a finitely generated projective module over a commutative ringReza Nekooei, Zahra PourshafieyλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒλ…Όλ¬Έμ§‘2019 Β· 제34ꢌ 제3호ON ΓΈ-SEMIPRIME SUBMODULESFatemeh Mirzaee, Mahdieh EbrahimpourλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒμ§€2017 Β· 제54ꢌ 제4호ON πœ™-w-FLAT MODULES AND THEIR HOMOLOGICAL DIMENSIONSWei Zhao, Xiaolei ZhangλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒλ³΄2021 Β· 제58ꢌ 제4호On ΓΈ-von Neumann regular ringsFanggui Wang, Gaohua Tang, Wei ZhaoλŒ€ν•œμˆ˜ν•™νšŒ Β· λŒ€ν•œμˆ˜ν•™νšŒμ§€2013 Β· 제50ꢌ 제1호

이 κ°„ν–‰λ¬Όμ˜ λ‹€λ₯Έ λ…Όλ¬Έ (13건)

The Ohm-Rush content function III: Completion, globalization, and power-content algebrasNeil Epstein, Jay Shapiropp. 1311-1325A Liouville theorem of an integral equation of the Chern-Simons-Higgs typeMengfan Ma, Yayun Li, Qinghua Chenpp. 1327-1345Bergman type operators on some generalized Cartan-Hartogs domainsLe He, Yanyan Tang, Zhenhan Tupp. 1347-1365Symmetric and pseudo-symmetric numerical semigroups via Young diagrams and their semigroup ringsMeral Suer, Mehmet Yesilpp. 1367-1383Some numerical radius inequalities for semi-Hilbert space operatorsKais Fekipp. 1385-1405
원문 보기