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WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS

Year 2020, , 43 - 60, 14.07.2020
https://doi.org/10.24330/ieja.768127

Abstract

Anderson-Smith studied weakly prime ideals for a commutative ring
with identity. Hirano, Poon and Tsutsui studied the structure of
a ring in which every ideal is weakly prime for rings, not
necessarily commutative. In this note we give some more properties
of weakly prime ideals in noncommutative rings. We introduce the
notion of a weakly prime radical of an ideal. We initiate the
study of weakly completely prime ideals and investigate
rings for which every proper ideal is weakly completely prime.

References

  • D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math., 29(4) (2003), 831-840.
  • A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
  • P. K. Beiranvand and R. Beyranvand, Almost prime and weakly prime submodules, J. Algebra Appl., 18(7) (2019), 1950129 (14 pp).
  • G. Birkenmeier, H. Heatherly and E. Lee, Prime ideals and prime radicals in near-rings, Monatsh. Math., 117 (1994), 179-197.
  • Y. Hirano, E. Poon and H. Tsutsui, On rings in which every ideal is weakly prime, Bull. Korean Math. Soc., 47(5) (2010), 1077-1087.
  • N. H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc., 8 (1957), 633-637.
  • S. Veldsman, A note on the radicals of idealizations, Southeast Asian Bull. Math., 32 (2008), 545-551.
Year 2020, , 43 - 60, 14.07.2020
https://doi.org/10.24330/ieja.768127

Abstract

References

  • D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math., 29(4) (2003), 831-840.
  • A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
  • P. K. Beiranvand and R. Beyranvand, Almost prime and weakly prime submodules, J. Algebra Appl., 18(7) (2019), 1950129 (14 pp).
  • G. Birkenmeier, H. Heatherly and E. Lee, Prime ideals and prime radicals in near-rings, Monatsh. Math., 117 (1994), 179-197.
  • Y. Hirano, E. Poon and H. Tsutsui, On rings in which every ideal is weakly prime, Bull. Korean Math. Soc., 47(5) (2010), 1077-1087.
  • N. H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc., 8 (1957), 633-637.
  • S. Veldsman, A note on the radicals of idealizations, Southeast Asian Bull. Math., 32 (2008), 545-551.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Nico Groenewald This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

APA Groenewald, N. (2020). WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. International Electronic Journal of Algebra, 28(28), 43-60. https://doi.org/10.24330/ieja.768127
AMA Groenewald N. WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. IEJA. July 2020;28(28):43-60. doi:10.24330/ieja.768127
Chicago Groenewald, Nico. “WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 43-60. https://doi.org/10.24330/ieja.768127.
EndNote Groenewald N (July 1, 2020) WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. International Electronic Journal of Algebra 28 28 43–60.
IEEE N. Groenewald, “WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS”, IEJA, vol. 28, no. 28, pp. 43–60, 2020, doi: 10.24330/ieja.768127.
ISNAD Groenewald, Nico. “WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS”. International Electronic Journal of Algebra 28/28 (July 2020), 43-60. https://doi.org/10.24330/ieja.768127.
JAMA Groenewald N. WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. IEJA. 2020;28:43–60.
MLA Groenewald, Nico. “WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 43-60, doi:10.24330/ieja.768127.
Vancouver Groenewald N. WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. IEJA. 2020;28(28):43-60.