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WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS

Year 2020, Volume 28, Issue 28, 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, Volume 28, Issue 28, 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.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Nico GROENEWALD This is me (Primary Author)
Nelson Mandela University
South Africa

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768127, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {43 - 60}, doi = {10.24330/ieja.768127}, title = {WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS}, key = {cite}, author = {Groenewald, Nico} }
APA Groenewald, N. (2020). WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS . International Electronic Journal of Algebra , 28 (28) , 43-60 . DOI: 10.24330/ieja.768127
MLA Groenewald, N. "WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS" . International Electronic Journal of Algebra 28 (2020 ): 43-60 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768127>
Chicago Groenewald, N. "WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS". International Electronic Journal of Algebra 28 (2020 ): 43-60
RIS TY - JOUR T1 - WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS AU - NicoGroenewald Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768127 DO - 10.24330/ieja.768127 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 43 EP - 60 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768127 UR - https://doi.org/10.24330/ieja.768127 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS %A Nico Groenewald %T WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768127 %U 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
AMA Groenewald N. WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. IEJA. 2020; 28(28): 43-60.
Vancouver Groenewald N. WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS. International Electronic Journal of Algebra. 2020; 28(28): 43-60.
IEEE N. Groenewald , "WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 43-60, Jul. 2020, doi:10.24330/ieja.768127