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ON RINGS IN WHICH EVERY IDEAL IS WEAKLY PRIME

  • Hirano, Yasuyuki ;
  • Poon, Edward ;
  • Tsutsui, Hisaya
  • Received : 2009.04.13
  • Accepted : 2009.10.01
  • Published : 2010.09.30

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.

Keywords

weakly prime

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