在有限稳定定义域上

IF 0.3 4区 数学 Q4 MATHEMATICS Journal of Commutative Algebra Pub Date : 2020-06-01 DOI:10.1216/jca.2020.12.179
Stefania Gabelli, M. Roitman
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引用次数: 3

摘要

结果表明:(1)一个局部阿基米德稳定域满足accp。(2)一个稳定定义域R是阿基米德的当且仅当R的每个非单位都属于R '的一个高度为1的素数理想(这个结果与普洱定义域的欧姆定理有关)。(3)阿基米德稳定域R是一维的当且仅当R '是等维的(一般来说,阿基米德稳定局部域不一定是一维的)。(4)具有稳定极大理想的阿基米德有限稳定半局部域是局部阿基米德域,但一般来说,阿基米德稳定域和阿基米德半局部域都不一定是局部阿基米德域。
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On finitely stable domains, II
Among other results, we prove the following: (1) A locally Archimedean stable domain satisfies accp. (2) A stable domain R is Archimedean if and only if every nonunit of R belongs to a height-one prime ideal of R′ (this result is related to Ohm’s Theorem for Prüfer domains). (3) An Archimedean stable domain R is one-dimensional if and only if R′ is equidimensional (generally, an Archimedean stable local domain is not necessarily onedimensional). (4) An Archimedean finitely stable semilocal domain with stable maximal ideals is locally Archimedean, but generally, neither Archimedean stable domains, nor Archimedean semilocal domains are necessarily locally Archimedean.
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来源期刊
CiteScore
0.80
自引率
16.70%
发文量
28
审稿时长
>12 weeks
期刊介绍: Journal of Commutative Algebra publishes significant results in the area of commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation theory, semigroups and monoids. The journal also publishes substantial expository/survey papers as well as conference proceedings. Any person interested in editing such a proceeding should contact one of the managing editors.
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RINGS WITH AN ELEMENTARY ABELIAN p-GROUP OF UNITS STRUCTURE OF THE KERNEL OF A LOCALLY NILPOTENT DERIVATION ON AN AFFINE NORMAL DOMAIN LATTICE DECOMPOSITION OF MODULES OVER COMMUTATIVE RINGS ON ABELIAN GROUPS HAVING ISOMORPHIC PROPER CHARACTERISTIC SUBGROUPS Author Index to Volume 15 (2023)
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