Papers by Mohamed Khalifa
Annali di Matematica Pura ed Applicata (1923 -), 2013
Let R be an APVD with maximal ideal M. We show that the power series ring R[[x 1 , . . . , x n ]]... more Let R be an APVD with maximal ideal M. We show that the power series ring R[[x 1 , . . . , x n ]] is an SFT-ring if and only if the integral closure of R is an SFT-ring if and only if (R is an SFT-ring and M is a Noether strongly primary ideal of (M : M)). We deduce that if R is an m-dimensional APVD that is a residually *-domain, then dim R[[x 1 , . . . , x n ]] = nm + 1 or nm + n.
Arabian Journal of Mathematics, 2014
We give necessary and sufficient conditions for the power series ring R[[x 1 ,. .. , x n ]] to be... more We give necessary and sufficient conditions for the power series ring R[[x 1 ,. .. , x n ]] to be a Jaffard domain, where R is an almost pseudo-valuation domain. Mathematics Subject Classification 13F25 • 13C15 • 13F05 • 13A15 All rings considered below are (commutative with identity) integral domains. The dimension of a ring R, denoted by dim R, means its Krull dimension. In [10], Jaffard defines the valuative dimension, denoted by dim v R, of an integral domain R to be the maximal rank of the valuation overrings of R. Following [1], an integral domain R is said to be a Jaffard ring if dim v R = dim R < ∞. Most standard examples of Jaffard domains are finite-dimensional Noetherian domains and finite-dimensional Prüfer domains [10]. In this paper, we are interested in when the power series ring R[[x]] is a Jaffard domain. It was shown by Arnold in [2] that if a ring R fails to have the SFT(strong finite type)-property, then R[[x]] has infinite dimension, and so has infinite valuative dimension. Recall that an ideal I of a ring R is an SFT-ideal if there exist a positive integer k and a finitely generated ideal F of R such that F ⊆ I and x k ∈ F for each x ∈ I ; moreover, if each ideal of R is an SFT-ideal, then we say that R is an SFT-ring. Let R be an integral domain. When is R[[x]] a Jaffard domain? The answer is known in two cases. First, if R is a Noetherian ring with finite dimension, then R[[x]] is also Noetherian with finite dimension [7, Lemma 2.6], and so a Jaffard domain. The second case was shown by Kang and Park. In [11], they computed the dimension of mixed extension R[x 1 ]]. .. [x n ]] where R is a finite dimensional SFT-Prüfer domain. In [15], Park generalized the result to the case, where R is a finite dimensional SFT-globalized pseudo-valuation domain (for short, GPVD) as shown in the following:
Isonoetherian power series rings
Communications in Algebra
ABSTRACT Facchini and Nazemian proved that a valuation domain is isonoetherian if and only if it ... more ABSTRACT Facchini and Nazemian proved that a valuation domain is isonoetherian if and only if it is discrete of Krull dimension ≤2 and they showed that this cannot be generalized from the local case to the global case: the 2-dimensional generalized Dedekind domain ℤ+Xℚ[[X]] is not isonoetherian. Let D be an integral domain with quotient field K. We provide necessary and sufficient conditions on D and K, so that the ring D+XK[[X]] is isonoetherian. We deduce that if D is integrally closed, then D+XK[[X]] is isonoetherian if and only if D is a semi-local principal ideal domain.
The current research intends to affirm the link between the Nile Valley and the depression that t... more The current research intends to affirm the link between the Nile Valley and the depression that thought to be the Bahariya River. To perform this target, shallow subsurface tectonic and geomorphic investigations of the basin northwest of Asyut using remote sensing and gravity data were carried out. Many image enhancement and transformation methods such as band combination, automatic stream extraction, and shaded relief were preceded to the remote sensing data such as Landsat-7 and Shuttle Radar Topography Mission (SRTM). Qualitative and quantitative analyses such as regional residual separation process, and derivatives maps were applied on gravity data to delineate structural trends. The result revealed a geomorphic and structure feature trend in NW–SE that consistent with the Nile segment between Qena to Asyut. This trend most likely connected to the structure event of the Nile Valley. Prominent uplift that detected by remote sensing and gravity data hindered the Bahariya River. Su...
Annali di Matematica Pura ed Applicata, 2012
Your article is protected by copyright and all rights are held exclusively by Fondazione Annali d... more Your article is protected by copyright and all rights are held exclusively by Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to selfarchive your work, please use the accepted author's version for posting to your own website or your institution's repository. You may further deposit the accepted author's version on a funder's repository at a funder's request, provided it is not made publicly available until 12 months after publication.
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Papers by Mohamed Khalifa