Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME

  • Hirano, Yasuyuki (DEPARTMENT OF MATHEMATICS NARUTO UNIVERSITY OF EDUCATION) ;
  • Poon, Edward (DEPARTMENT OF MATHEMATICS EMBRY-RIDDLE AERONAUTICAL UNIVERSITY) ;
  • Tsutsui, Hisaya (DEPARTMENT OF MATHEMATICS EMBRY-RIDDLE AERONAUTICAL UNIVERSITY)
  • Received : 2009.04.13
  • Accepted : 2009.10.01
  • Published : 2010.09.30
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Abstract

Anderson-Smith [1] studied weakly prime ideals for a commutative ring with identity. Blair-Tsutsui [2] studied the structure of a ring in which every ideal is prime. In this paper we investigate the structure of rings, not necessarily commutative, in which all ideals are weakly prime.

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References

  1. D. D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 29 (2003), no. 4, 831-840.
  2. W. D. Blair and H. Tsutsui, Fully prime rings, Comm. Algebra 22 (1994), no. 13, 5389-5400. https://doi.org/10.1080/00927879408825136
  3. K. Koh, On one sided ideals of a prime type, Proc. Amer. Math. Soc. 28 (1971), 321-329. https://doi.org/10.1090/S0002-9939-1971-0274488-5
  4. H. Tsutsui, Fully prime rings. II, Comm. Algebra 24 (1996), no. 9, 2981-2989. https://doi.org/10.1080/00927879608825725

Cited by

  1. Almost prime submodules pp.1793-7183, 2018, https://doi.org/10.1142/S1793557120500199