Every commutative ring has a minimal ring extension

Communications in Algebra

Volumn 34, Issue 10, 2006, Pages 3875-3881

  Dobbs, David E ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Idealization; Integral domain; Maximal Ideal; Minimal ring extension; Overring; Simple module; Total quotient ring

Indexed keywords

EID: 33845866333     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927870600862706     Document Type: Article

References (11)

1. Anderson, D. D. (2001). Cancellation modules and related modules. In: Anderson, D. D., Papick, I. J., eds. Ideal Theoretic Methods in Commutative Algebra. New York: Dekker, pp. 13-25.
2. Ayache, A. (2003). Minimal overrings of an integrally closed domain. Comm. Algebra 31:5693-5714.
3. Badawi, A. (2003). On Φ-pseudo-valuation rings. II. (2000). Houston J. Math. 26:473-480.
4. Dobbs, D. E. (1976). Divided rings and going-down. Pac. J. Math. 67:353-363.
5. Ferrand, D., Olivier, J.-P. (1970). Morphismes minimaux d'anneaux. J. Algebra 16:461-471.
6. Gilmer, R., Heinzer, W. (1967). Intersections of quotient rings of an integral domain. J. Math. Kyoto Univ. 7:133-150.
7. Kabbaj, S.-E., Mahdou, N. (2004). Trivial extensions defined by coherent-like conditions. Comm. Algebra 32:3937-3953.
8. Kaplansky, I. (1974). Topics in Commutative Ring Theory. Chicago: Univ. Chicago Press.
9. Nagata, M. (1962). Local Rings. New York: Wiley-Interscience.
10. Papick, I. J. (1976). Local minimal overrings Can. J. Math. 27:788-792.
11. Sato, J., Sugatani, T., Yochida, K. I. (1992). On minimal overrings of a Noetherian domain. Comm. Algebra 20:1746-1753.