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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2020.1
- 수록면
- 53 - 69 (17page)
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Let (A, M) ⊂ (B, N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N. Suppose henceforth that M ⊆ N. If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A + N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite field.
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참고문헌 (27)
참고문헌 신청
M. F. Atiyah / 1969 / Introduction to commutative algebra / AddisonWesley
J.-P. Cahen / 2011 / Characterizing minimal ring extensions / Rocky Mountain J. Math 41:1081~1125
S. U. Chase / 1965 / Galois theory and Galois cohomology of commutative rings / Mem. Amer. Math. Soc 52:15~33
P. M. Cohn / 1968 / Bezout rings and their subrings / Proc. Cambridge Philos. Soc 64:251~264
D. L. Costa / 1977 / Retracts of polynomial rings / J. Algebra 44:492~502
J.-P. Cahen / 2011 / Characterizing minimal ring extensions / Rocky Mountain J. Math 41:1081~1125
S. U. Chase / 1965 / Galois theory and Galois cohomology of commutative rings / Mem. Amer. Math. Soc 52:15~33
P. M. Cohn / 1968 / Bezout rings and their subrings / Proc. Cambridge Philos. Soc 64:251~264
D. L. Costa / 1977 / Retracts of polynomial rings / J. Algebra 44:492~502
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