scholarly journals m-full ideals

1987 ◽  
Vol 106 ◽  
pp. 101-111 ◽  
Author(s):  
Junzo Watanabe
Keyword(s):  
Local Ring ◽  
Dimensional Case ◽  
Flat Extension ◽  
Basic Properties ◽  
Number Of Generators ◽  
Low Dimensional

An ideal a of a local ring (R, m) is called m-full if am: y = a for some y in a certain faithfully flat extension of R. The definition is due to Rees (unpublished) and he had obtained some elementary results (also unpublished). The present paper concerns some basic properties of m-full ideals. One result is the characterization of m-fullness in terms of the minimal number of generators of ideal, generalizing his result in a low dimensional case (Theorem 2, § 2).

Characterization of low dimensional molybdenum sulfide nanostructures

2008 ◽  
Vol 59 (3) ◽  
pp. 204-212 ◽  
Author(s):  
G. Alejandra Camacho-Bragado ◽  
Jose Luis Elechiguerra ◽  
Miguel Jose Yacaman
Keyword(s):  
Molybdenum Sulfide ◽  
Low Dimensional

scholarly journals Low-dimensional dynamical characterization of human performance of cancer patients using motion data

2018 ◽  
Vol 56 ◽  
pp. 61-69 ◽  
Author(s):  
Zaki Hasnain ◽  
Ming Li ◽  
Tanya Dorff ◽  
David Quinn ◽  
Naoto T. Ueno ◽  
...  
Keyword(s):  
Cancer Patients ◽  
Human Performance ◽  
Motion Data ◽  
Low Dimensional

scholarly journals A Characterization of Gorenstein Rings and Grothendieck's Conjecture

2009 ◽  
Vol 16 (04) ◽  
pp. 653-660
Author(s):  
Kazem Khashyarmanesh
Keyword(s):  
Local Ring ◽  
Regular Sequence ◽  
Negative Integer ◽  
Finitely Generated ◽  
Gorenstein Rings ◽  
Noetherian Local Ring ◽  
Filter Regular Sequence ◽  
System Of Parameters

Given a commutative Noetherian local ring (R, 𝔪), it is shown that R is Gorenstein if and only if there exists a system of parameters x1,…,xd of R which generates an irreducible ideal and [Formula: see text] for all t > 0. Let n be an arbitrary non-negative integer. It is also shown that for an arbitrary ideal 𝔞 of a commutative Noetherian (not necessarily local) ring R and a finitely generated R-module M, [Formula: see text] is finitely generated if and only if there exists an 𝔞-filter regular sequence x1,…,xn∈ 𝔞 such that [Formula: see text] for all t > 0.

scholarly journals Normal Toeplitz Operators on the Bergman Space

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1463
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Basic Properties

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).

scholarly journals A Note on Gorenstein Rings of Embedding Codimension Three

1973 ◽  
Vol 50 ◽  
pp. 227-232 ◽  
Author(s):  
Junzo Watanabe
Keyword(s):  
Local Ring ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Regular Sequence ◽  
Complete Intersections ◽  
Gorenstein Ring ◽  
Regular Local Ring ◽  
Gorenstein Rings ◽  
Number Of Generators ◽  
Five Elements

Let A = R/, where R is a regular local ring of arbitrary dimension and is an ideal of R. If A is a Gorenstein ring and if height = 2, it is easily proved that A is a complete intersection, i.e., is generated by two elements (Serre [5], Proposition 3). Hence Gorenstein rings which are not complete intersections are of embedding codimension at least three. An example of these rings is found in Bass’ paper [1] (p. 29). This is obtained as a quotient of a three dimensional regular local ring by an ideal which is generated by five elements, i.e., generated by a regular sequence plus two more elements. In this paper, suggested by this example, we prove that if A is a Gorenstein ring and if height = 3, then is minimally generated by an odd number of elements. If A has a greater codimension, presumably there is no such restriction on the minimal number of generators for , as will be conceived from the proof.

scholarly journals Intrinsic Effect of Pyridine-N-Position on Structural Properties of Cu-Based Low-Dimensional Coordination Frameworks

2020 ◽  
Vol 21 (17) ◽  
pp. 6171
Author(s):  
Anna Walczak ◽  
Gracjan Kurpik ◽  
Artur R. Stefankiewicz
Keyword(s):  
Physicochemical Characterization ◽  
Pyridine Nitrogen ◽  
Nitrogen Donor ◽  
Metal Organic ◽  
Low Dimensional ◽  
Polymeric Assemblies ◽  
Organic Assemblies ◽  
Intrinsic Effect ◽  
Supramolecular Aggregates

Metal-organic assemblies have received significant attention for catalytic and other applications, including gas and energy storage, due to their porosity and thermal/chemical stability. Here, we report the synthesis and physicochemical characterization of three metallosupramolecular assemblies consisting of isomeric ambidentate pyridyl-β-diketonate ligands L1–L3 and Cu(II) metal ions. It has been demonstrated that the topology and dimensionality of generated supramolecular aggregates depend on the location of the pyridine nitrogen donor atom in L1–L3. This is seen in characterization of two distinct 2D polymeric assemblies, i.e., [Cu(L1)2]n and [Cu(L2)2]n, in which both β-diketonate and pyridine groups are coordinated to the Cu(II) center, as well as in characterization of the mononuclear 1D complex Cu(L3)2, in which the central atom is bound only by two β-diketonate units.

scholarly journals Thermal Characterization of Low-Dimensional Materials by Resistance Thermometers

Materials ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 1740 ◽  
Author(s):  
Yifeng Fu ◽  
Guofeng Cui ◽  
Kjell Jeppson
Keyword(s):  
Thermal Performance ◽  
Three Dimensional ◽  
Thermal Characterization ◽  
Resistance Thermometer ◽  
Light Emitting ◽  
Resistance Thermometers ◽  
Low Dimensional ◽  
Low Dimensional Materials ◽  
Boron Nitride Films

The design, fabrication, and use of a hotspot-producing and temperature-sensing resistance thermometer for evaluating the thermal properties of low-dimensional materials are described in this paper. The materials that are characterized include one-dimensional (1D) carbon nanotubes, and two-dimensional (2D) graphene and boron nitride films. The excellent thermal performance of these materials shows great potential for cooling electronic devices and systems such as in three-dimensional (3D) integrated chip-stacks, power amplifiers, and light-emitting diodes. The thermometers are designed to be serpentine-shaped platinum resistors serving both as hotspots and temperature sensors. By using these thermometers, the thermal performance of the abovementioned emerging low-dimensional materials was evaluated with high accuracy.

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