Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A NOTE ON REAL QUATERNION

  • Received : 2009.05.12
  • Published : 2009.06.30
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Abstract

We consider pm-ring with the property such that every prime ideal is contained in only one maximal ideal. Orsatti[4] characterized pm-rings by means of the retraction. Contessa[1] found algebraic condition, by using that direct product of pm-rings is a pm-ring. We show that C(X, H) and C(X, C) are pm-rings and we extend a quasi pm-domain.

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References

  1. Maria Contessa, On pm-rings, Comm. Algebra, 10(1), 1982, 93-108. https://doi.org/10.1080/00927878208822703
  2. Myung-sook Ahn and D. D. Anderson, Weakly clean rings and almost clean rings, Rocky mountain J. Math. 36(3)(2006), 783-798. https://doi.org/10.1216/rmjm/1181069429
  3. Hu-Hao Sun, Noncommutative rings in which every prime ideal is contained in a unique maximal ideal, Journal of Pure and Appl. Algebra 76(1991), 179-192. North-Holland. https://doi.org/10.1016/0022-4049(91)90060-F
  4. Giuseppe de Marco and Adaiberto Orsatti, Commutative Rings in which every prime ideal is contained in a uniqe maximal ideal, Proc. Amer. Math. Soc., 30(1971) 459-466. https://doi.org/10.1090/S0002-9939-1971-0282962-0
  5. M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addition Wesly, 1968.