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Volumn 308, Issue 2, 2007, Pages 800-821

A classification of the minimal ring extensions of certain commutative rings

Author keywords

Divided prime ideal; Idealization; Integrality; Kaplansky transform; Minimal ring extension; Overring; Reduced ring; Total quotient ring; von Neumann regular ring

Indexed keywords


EID: 33751410362     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2006.07.024     Document Type: Article
Times cited : (39)

References (21)
  • 1
    • 0035982307 scopus 로고    scopus 로고
    • Divisibility conditions in commutative rings with zerodivisors
    • Anderson D.F., and Badawi A. Divisibility conditions in commutative rings with zerodivisors. Comm. Algebra 30 (2002) 4031-4047
    • (2002) Comm. Algebra , vol.30 , pp. 4031-4047
    • Anderson, D.F.1    Badawi, A.2
  • 2
    • 0242509885 scopus 로고    scopus 로고
    • Minimal overrings of an integrally closed domain
    • Ayache A. Minimal overrings of an integrally closed domain. Comm. Algebra 31 (2003) 5693-5714
    • (2003) Comm. Algebra , vol.31 , pp. 5693-5714
    • Ayache, A.1
  • 3
    • 0033240684 scopus 로고    scopus 로고
    • On divided commutative rings
    • Badawi A. On divided commutative rings. Comm. Algebra 27 (1999) 1465-1474
    • (1999) Comm. Algebra , vol.27 , pp. 1465-1474
    • Badawi, A.1
  • 4
    • 0035535725 scopus 로고    scopus 로고
    • On locally divided rings and going-down rings
    • Badawi A., and Dobbs D.E. On locally divided rings and going-down rings. Comm. Algebra 29 (2001) 2805-2825
    • (2001) Comm. Algebra , vol.29 , pp. 2805-2825
    • Badawi, A.1    Dobbs, D.E.2
  • 5
    • 33751397845 scopus 로고    scopus 로고
    • L.I. Dechéne, Adjacent extensions of rings, PhD dissertation, University of California, Riverside, 1978
  • 6
    • 0007235974 scopus 로고    scopus 로고
    • Going-down rings with zero-divisors
    • Dobbs D.E. Going-down rings with zero-divisors. Houston J. Math. 23 (1997) 1-12
    • (1997) Houston J. Math. , vol.23 , pp. 1-12
    • Dobbs, D.E.1
  • 7
    • 33751408643 scopus 로고    scopus 로고
    • D.E. Dobbs, Every commutative ring has a minimal ring extension, Comm. Algebra, in press
  • 8
    • 33751424005 scopus 로고    scopus 로고
    • D.E. Dobbs, A sufficient condition for a minimal ring extension to be an overring, Comm. Algebra, in press
  • 10
    • 33748685413 scopus 로고    scopus 로고
    • A classification of the minimal ring extensions of an integral domain
    • Dobbs D.E., and Shapiro J. A classification of the minimal ring extensions of an integral domain. J. Algebra 305 1 (2006) 185-193
    • (2006) J. Algebra , vol.305 , Issue.1 , pp. 185-193
    • Dobbs, D.E.1    Shapiro, J.2
  • 11
    • 0013485045 scopus 로고
    • Homomorphismes minimaux d'anneaux
    • Ferrand D., and Olivier J.-P. Homomorphismes minimaux d'anneaux. J. Algebra 16 (1970) 461-471
    • (1970) J. Algebra , vol.16 , pp. 461-471
    • Ferrand, D.1    Olivier, J.-P.2
  • 12
    • 0001283281 scopus 로고
    • Topologically defined classes of commutative rings
    • Fontana M. Topologically defined classes of commutative rings. Ann. Mat. Pura Appl. 123 (1980) 331-355
    • (1980) Ann. Mat. Pura Appl. , vol.123 , pp. 331-355
    • Fontana, M.1
  • 13
    • 33751433772 scopus 로고    scopus 로고
    • M.S. Gilbert, Extensions of commutative rings with linearly ordered intermediate rings, PhD dissertation, University of Tennessee, Knoxville, 1996
  • 15
    • 0003311025 scopus 로고
    • Commutative Coherent Rings
    • Springer-Verlag, Berlin
    • Glaz S. Commutative Coherent Rings. Lecture Notes in Math. vol. 1371 (1989), Springer-Verlag, Berlin
    • (1989) Lecture Notes in Math. , vol.1371
    • Glaz, S.1
  • 20
    • 84946621980 scopus 로고
    • On minimal overrings of a Noetherian domain
    • Sato J., Sugatani T., and Yoshida K.I. On minimal overrings of a Noetherian domain. Comm. Algebra 20 (1992) 1735-1746
    • (1992) Comm. Algebra , vol.20 , pp. 1735-1746
    • Sato, J.1    Sugatani, T.2    Yoshida, K.I.3
  • 21
    • 33751403022 scopus 로고    scopus 로고
    • J. Shapiro, Flat epimorphisms and a generalized Kaplansky ideal transform, Rocky Mountain J. Math., in press


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.