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Quasi-$n$-absorbing and semi-$n$-absorbing preradicals

Year 2019, Volume: 48 Issue: 5, 1286 - 1303, 08.10.2019
https://doi.org/10.15672/hujms.592974

Abstract

The aim of this paper is to introduce the notions of quasi-$n$-absorbing preradicals and of semi-$n$-absorbing preradicals. These notions are inspired by applying the concept of $n$-absorbing preradicals to semiprime preradicals. Also, we study the concepts of quasi-$n$-absorbing submodules and of semi-$n$-absorbing submodules and their relations with quasi-$n$-absorbing preradicals and semi-$n$-absorbing preradicals.

References

  • [1] D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39, 1646–1672, 2011.
  • [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75, 417–429, 2007.
  • [3] J. Beachy, M-injective modules and prime M-ideals, Comm. Algebra 30 (10), 4649– 4676, 2002.
  • [4] L. Bican, P. Jambor, T. Kepka and P. Nemec, Preradicals, Comment. Math. Univ. Carolinae 15 (1), 75–83, 1974.
  • [5] L. Bican, P. Jambor, T. Kepka and P. Nemec, Prime and coprime modules, Fund. Math. 107, 33–45, 1980.
  • [6] L. Bican, T. Kepka, and P. Nemec, Rings, Modules and Preradicals, Marcel Dekker, New York, 1982.
  • [7] A.I. Kashu, On some operations in the lattice of submodules determined by preradi- cals, Bull. Acad. Stiinte Repub. Mold. Mat. 2 (66), 5–16, 2011.
  • [8] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer-Verlag, 1998.
  • [9] F. Raggi, J. Ríos, H. Rincón and R. Fernández-Alonso, Basic preradicals and main injective modules, J. Algebra Appl. 8 (1), 1–16, 2009.
  • [10] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra 30 (3), 1533–1544, 2002.
  • [11] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals II : partitions, J. Algebra Appl. 1 (2), 201–214, 2002.
  • [12] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals III : operators, J. Pure and Applied Algebra 190, 251–265, 2004.
  • [13] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4 (4), 451–466, 2005.
  • [14] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Semiprime preradicals, Comm. Algebra 37, 2811–2822, 2009.
  • [15] B. Stenström, Rings of Quotients, Die Grundlehren der Mathematischen Wis- senschaften, Band 217, Springer Verlag, Berlin, 1975.
  • [16] D. Keskin Tütüncü and Y. Kuratomi, On mono-injective modules and mono-ojective modules, Math. J. Okayama Univ. 55, 117–129, 2013.
  • [17] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.
  • [18] A. Yousefian Darani, and H. Mostafanasab, Co-2-absorbing preradicals and submod- ules, J. Algebra Appl. 14 (7), 1550113 (23 pages), 2015.
  • [19] A. Yousefian Darani and H. Mostafanasab, On 2-absorbing preradicals, J. Algebra Appl. 14 (2), 1550017 (22 pages), 2015.
  • [20] A. Yousefian Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submod- uels, Thai J. Math. 9 (3), 577–584, 2011.
Year 2019, Volume: 48 Issue: 5, 1286 - 1303, 08.10.2019
https://doi.org/10.15672/hujms.592974

Abstract

References

  • [1] D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39, 1646–1672, 2011.
  • [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75, 417–429, 2007.
  • [3] J. Beachy, M-injective modules and prime M-ideals, Comm. Algebra 30 (10), 4649– 4676, 2002.
  • [4] L. Bican, P. Jambor, T. Kepka and P. Nemec, Preradicals, Comment. Math. Univ. Carolinae 15 (1), 75–83, 1974.
  • [5] L. Bican, P. Jambor, T. Kepka and P. Nemec, Prime and coprime modules, Fund. Math. 107, 33–45, 1980.
  • [6] L. Bican, T. Kepka, and P. Nemec, Rings, Modules and Preradicals, Marcel Dekker, New York, 1982.
  • [7] A.I. Kashu, On some operations in the lattice of submodules determined by preradi- cals, Bull. Acad. Stiinte Repub. Mold. Mat. 2 (66), 5–16, 2011.
  • [8] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer-Verlag, 1998.
  • [9] F. Raggi, J. Ríos, H. Rincón and R. Fernández-Alonso, Basic preradicals and main injective modules, J. Algebra Appl. 8 (1), 1–16, 2009.
  • [10] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra 30 (3), 1533–1544, 2002.
  • [11] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals II : partitions, J. Algebra Appl. 1 (2), 201–214, 2002.
  • [12] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals III : operators, J. Pure and Applied Algebra 190, 251–265, 2004.
  • [13] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4 (4), 451–466, 2005.
  • [14] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Semiprime preradicals, Comm. Algebra 37, 2811–2822, 2009.
  • [15] B. Stenström, Rings of Quotients, Die Grundlehren der Mathematischen Wis- senschaften, Band 217, Springer Verlag, Berlin, 1975.
  • [16] D. Keskin Tütüncü and Y. Kuratomi, On mono-injective modules and mono-ojective modules, Math. J. Okayama Univ. 55, 117–129, 2013.
  • [17] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.
  • [18] A. Yousefian Darani, and H. Mostafanasab, Co-2-absorbing preradicals and submod- ules, J. Algebra Appl. 14 (7), 1550113 (23 pages), 2015.
  • [19] A. Yousefian Darani and H. Mostafanasab, On 2-absorbing preradicals, J. Algebra Appl. 14 (2), 1550017 (22 pages), 2015.
  • [20] A. Yousefian Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submod- uels, Thai J. Math. 9 (3), 577–584, 2011.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Hojjat Mostafanasab This is me 0000-0002-1690-0607

Ahmad Yousefian Darani 0000-0002-7411-8621

Publication Date October 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 5

Cite

APA Mostafanasab, H., & Yousefian Darani, A. (2019). Quasi-$n$-absorbing and semi-$n$-absorbing preradicals. Hacettepe Journal of Mathematics and Statistics, 48(5), 1286-1303. https://doi.org/10.15672/hujms.592974
AMA Mostafanasab H, Yousefian Darani A. Quasi-$n$-absorbing and semi-$n$-absorbing preradicals. Hacettepe Journal of Mathematics and Statistics. October 2019;48(5):1286-1303. doi:10.15672/hujms.592974
Chicago Mostafanasab, Hojjat, and Ahmad Yousefian Darani. “Quasi-$n$-Absorbing and Semi-$n$-Absorbing Preradicals”. Hacettepe Journal of Mathematics and Statistics 48, no. 5 (October 2019): 1286-1303. https://doi.org/10.15672/hujms.592974.
EndNote Mostafanasab H, Yousefian Darani A (October 1, 2019) Quasi-$n$-absorbing and semi-$n$-absorbing preradicals. Hacettepe Journal of Mathematics and Statistics 48 5 1286–1303.
IEEE H. Mostafanasab and A. Yousefian Darani, “Quasi-$n$-absorbing and semi-$n$-absorbing preradicals”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, pp. 1286–1303, 2019, doi: 10.15672/hujms.592974.
ISNAD Mostafanasab, Hojjat - Yousefian Darani, Ahmad. “Quasi-$n$-Absorbing and Semi-$n$-Absorbing Preradicals”. Hacettepe Journal of Mathematics and Statistics 48/5 (October 2019), 1286-1303. https://doi.org/10.15672/hujms.592974.
JAMA Mostafanasab H, Yousefian Darani A. Quasi-$n$-absorbing and semi-$n$-absorbing preradicals. Hacettepe Journal of Mathematics and Statistics. 2019;48:1286–1303.
MLA Mostafanasab, Hojjat and Ahmad Yousefian Darani. “Quasi-$n$-Absorbing and Semi-$n$-Absorbing Preradicals”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, 2019, pp. 1286-03, doi:10.15672/hujms.592974.
Vancouver Mostafanasab H, Yousefian Darani A. Quasi-$n$-absorbing and semi-$n$-absorbing preradicals. Hacettepe Journal of Mathematics and Statistics. 2019;48(5):1286-303.