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논문 기본 정보
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- 학술저널
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- 2011.1
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Let (R; T) be a normal pair of commutative rings (i.e., R T is a unital extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R S T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the \if" part of the assertion fails if P is taken to be the \divided domain" property.
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참고문헌 (24)
참고문헌 신청
A. Badawi / 1999 / On divided commutative rings / Comm. Algebra 27 : 1465 ~ 1474
A. Badawi / 2001 / On locally divided rings and going-down rings / Comm. Algebra 29 : 2805 ~ 2825
D. E. Dobbs / / Normal pairs with zero-divisors / J. Algebra Appl
D. E. Dobbs / 1974 / On going-down for simple overrings, II / Comm. Algebra 1 : 439 ~ 458
D. E. Dobbs / 1976 / Divided rings and going-down / Pac. J. Math 67 : 353 ~ 363
A. Badawi / 2001 / On locally divided rings and going-down rings / Comm. Algebra 29 : 2805 ~ 2825
D. E. Dobbs / / Normal pairs with zero-divisors / J. Algebra Appl
D. E. Dobbs / 1974 / On going-down for simple overrings, II / Comm. Algebra 1 : 439 ~ 458
D. E. Dobbs / 1976 / Divided rings and going-down / Pac. J. Math 67 : 353 ~ 363
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