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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 817 - 826 (10page)
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Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R=K. We say that R has property (＊) if for each nonzero element a in R, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (＊), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (＊) if and only if R has no R-sequence of length 2, the " if " assertion fails in general for non-domain rings R. Each treed domain has property (＊), but the converse is false.
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참고문헌 (14)
참고문헌 신청
D. D. Anderson. / 2007 / Monoid domain construc-tions of antimatter domains / Comm. Algebra 35 : 3236 ~ 3241
D. E. Dobbs / 1974 / On going-down for simple overrings, II / Comm. Algebra 1 : 439 ~ 458
D. E. Dobbs / 1978 / Coherence, ascent of going-down and pseudo-valuation domains / Hous-ton J. Math 4 : 551 ~ 567
D. E. Dobbs / 2003 / Treed domains have grade 1, Internat / J. Commut. Rings 2 : 43 ~ 46
D. F. Anderson. / 1980 / Pairs of rings with the same prime ideals / Canad. Math. J 2 : 363 ~ 384
D. E. Dobbs / 1974 / On going-down for simple overrings, II / Comm. Algebra 1 : 439 ~ 458
D. E. Dobbs / 1978 / Coherence, ascent of going-down and pseudo-valuation domains / Hous-ton J. Math 4 : 551 ~ 567
D. E. Dobbs / 2003 / Treed domains have grade 1, Internat / J. Commut. Rings 2 : 43 ~ 46
D. F. Anderson. / 1980 / Pairs of rings with the same prime ideals / Canad. Math. J 2 : 363 ~ 384
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