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A note on real quaternion
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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.
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.
참고문헌 (5)
- Maria Contessa, "On pm-rings", Comm. Algebra, 10(1), pp.93~108 (1982)
- Myung-sook Ahn, "Weakly clean rings and almost clean rings", Rocky mountain J. Math., 36(3), pp.783~798 (2006)
- Hu-Hao Sun, "Noncommutative rings in which every prime ideal is contained in a unique maximal ideal", Journal of Pure and Appl. Algebra, 76, pp.179~192 (1991)
- Giuseppe de Marco, "Commutative Rings in which ev-ery prime ideal is contained in a uniqe maximal ideal", Proc. Amer. Math. Soc, 30, pp.459~466 (1971)
- M. F. Atiyah, "Introduction to commutative algebra" (1968), Addition Wesly
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