본문 바로가기
KERD
논문KCI 등재

Torsion modules and spectral spaces

Hajar Roshan-Shekalgourabi
대한수학회 (The Korean Mathematical Society)|2019.01|대한수학회논문집 (Communications of the KMS)|제34권 제1호|pp. 95-103|DOI 10.4134/CKMS.c180018

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Zariski topologyspectral spacetorsion modulesprime submodules
주제분류수학

초록

In this paper we study certain modules whose prime spectrums are Noetherian or/and spectral spaces. In particular, we investigate the relationship between topological properties of prime spectra of torsion modules and algebraic properties of them.

Abstract

In this paper we study certain modules whose prime spectrums are Noetherian or/and spectral spaces. In particular, we investigate the relationship between topological properties of prime spectra of torsion modules and algebraic properties of them.

참고문헌 (27)

  1. A. Abbasi, "Modules and spectral spaces", Comm. Algebra, 40(11), pp.4111~4129 (2012)
  2. J. Abuhlail, "A dual Zariski topology for modules", Topology Appl, 158(3), pp.457~467 (2011)
  3. H. Ansari-Toroghy, "On the prime spectrum of top mod-ules", Algebra Discrete Math, 11(1), pp.1~16 (2011)
  4. H. Ansari-Toroghy, "On the prime spectrum of X-injective modules", Comm. Algebra, 38(7), pp.2606~2621 (2010)
  5. M. F. Atiyah, "Introduction to Commutative Algebra" (1969), Addison-Wesley Publishing Co
  6. M. Behboodi, "Classical Zariski topology of modules and spectral spaces. I", Int. Electron. J. Algebra, 4, pp.104~130 (2008)
  7. M. Behboodi, "Classical Zariski topology of modules and spectral spaces. II", Int. Electron. J. Algebra, 4, pp.131~148 (2008)
  8. M. P. Brodmann, "Local Cohomology: An Algebraic Introduction with Geometric Applications" (1998), Cambridge University Press
  9. T. Duraivel, "Topology on spectrum of modules", J. Ramanujan Math. Soc, 9(1), pp.25~34 (1994)
  10. D. Hassanzadeh-Lelekaami, "Prime submodules and a sheaf on the prime spectra of modules", Comm. Algebra, 42(7), pp.3063~3077 (2014)
  11. Dawood Hassanzadeh-Lelekaami, "On Regular Modules over Commutative Rings", Bulletin of the Malaysian Mathematical Sciences Society, 42(2), pp.569~583 (2019), Springer Science and Business Media LLC[DOI]
  12. M. Hochster, "Prime ideal structure in commutative rings", Trans. Amer. Math. Soc, 142, pp.43~60 (1969)
  13. C. -P. Lu, "Prime submodules of modules", Comment. Math. Univ. St. Paul, 33(1), pp.61~69 (1984)
  14. C. -P. Lu, "M-radicals of submodules in modules", Math. Japon, 34(2), pp.211~219 (1989)
  15. C. -P. Lu, "Spectra of modules", Comm. Algebra, 23(10), pp.3741~3752 (1995)
  16. C. -P. Lu, "The Zariski topology on the prime spectrum of a module", Houston J. Math, 25(3), pp.417~432 (1999)
  17. C. -P. Lu, "A module whose prime spectrum has the surjective natural map", Houston J. Math, 33(1), pp.125~143 (2007)
  18. C. -P. Lu, "Modules with Noetherian spectrum", Comm. Algebra, 38(3), pp.807~828 (2010)
  19. R. L. McCasland, "On radicals of submodules", Comm. Algebra, 19(5), pp.1327~1341 (1991)
  20. R. L. McCasland, "Prime submodules", Comm. Algebra, 20(6), pp.1803~1817 (1992)
  21. R. L. McCasland, "On the spectrum of a module over a commutative ring", Comm. Algebra, 25(1), pp.79~103 (1997)
  22. R. L. McCasland, "An introduction to Zariski spaces over Zariski topologies", Rocky Mountain J. Math, 28(4), pp.1357~1369 (1998)
  23. C. Peskine, "An Algebraic Introduction to Complex Projective Geometry. 1" (1996), Cambridge University Press
  24. J. J. Rotman, "An Introduction to Homological Algebra" (1979), Academic Press, Inc
  25. R. Y. Sharp, "Steps in Commutative Algebra" (2000), Cambridge University Press
  26. Ü. Tekir, "On the sheaf of modules", Comm. Algebra, 33(8), pp.2557~2562 (2005)
  27. G. Zhang, "Multiplication modules in which every prime sub-module is contained in a unique maximal submodule", Comm. Algebra, 32(5), pp.1945~1959 (2004)

관련 논문AI추천

Topological dimension of pseudo-prime spectrum of modulesDawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi대한수학회 · 대한수학회논문집2017 · 제32권 제3호On the Classical Zariski Topology Over Prime Spectrum of a ModuleMUSTAFA ALKAN, Seçil ÇEKEN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호Second classical Zariski topology on second spectrum of lattice modulesNarayan Phadatare, Pradip Girase, Vandeo Borkar강원경기수학회 · 한국수학논문집2020 · 제28권 제3호On Noetherian pseudo-prime spectrum of a topological le-moduleAnjan Kumar Bhuniya, Manas Kumbhakar대한수학회 · 대한수학회논문집2023 · 제38권 제1호The homogeneous spectrum of a graded commutative ring by torsion groupMohamed Aqalmoun, Yassir Mata대한수학회 · 대한수학회보2025 · 제62권 제1호Notes on finitely generated flat modulesAbolfazl Tarizadeh대한수학회 · 대한수학회보2020 · 제57권 제2호

이 간행물의 다른 논문 (26건)

Some new identities concerning the Horadam sequence and its companion sequenceZafer Siar, Refik Keskinpp. 1-16Structure of $3$-prime near-rings satisfying some identitiesAbdelkarim Bouapp. 17-26Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10Ayse Alaca, Mada Altiarypp. 27-41Symmetric property of rings with respect to the Jacobson radicalTugce Pekacar Calci, Abdullah Harmanci, Sait Halicioglupp. 43-54Solutions and stability of trigonometric functional equations on an amenable group with an involutive automorphismOmar Ajebbar, Elhoucien Elqorachipp. 55-82
원문 보기