Super height of an ideal in a Noetherian ring
نویسندگان
چکیده
منابع مشابه
Notes on amalgamated duplication of a ring along an ideal
In this paper, we study some ring theoretic properties of the amalgamated duplication ring $Rbowtie I$ of a commutative Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$ satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a normal ring, a generalized Cohen-Macaulay ring and finally a filter ring.
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Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. T...
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In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.
متن کاملnotes on amalgamated duplication of a ring along an ideal
in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.
متن کاملThe annihilator-inclusion Ideal graph of a commutative ring
Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90194-9