Topological properties of the prime spectrum of a semimodule

2021 ◽  
Vol 566 ◽  
pp. 205-221
Author(s):  
Song-Chol Han ◽  
Won-Sok Pae ◽  
Jin-Nam Ho
Keyword(s):  
Topological Properties ◽  
Prime Spectrum

Zariski Topologies on Graded Ideals

2021 ◽  
Vol 78 (1) ◽  
pp. 215-224
Author(s):  
Malik Bataineh ◽  
Azzh Saad Alshehry ◽  
Rashid Abu-Dawwas
Keyword(s):  
Commutative Ring ◽  
Zariski Topology ◽  
Topological Properties ◽  
Prime Spectrum ◽  
Algebraic Properties

Abstract In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense, and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.

A localic approach to minimal prime spectra

1988 ◽  
Vol 103 (1) ◽  
pp. 47-53 ◽  
Author(s):  
Sun Shu-Hao
Keyword(s):  
Distributive Lattice ◽  
Prime Ideals ◽  
Zariski Topology ◽  
Topological Properties ◽  
Prime Spectrum ◽  
Minimal Prime

Throughout this paper, A will denote a distributive lattice with 0 and 1; we shall write spec A for the prime spectrum of A (i.e. the set of prime ideals of A, with the Stone–Zariski topology), and max A, min A for the subspaces of spec A consisting of maximal and minimal prime ideals respectively. These two subspaces have rather different topological properties: max A is always compact, but not always Hausdorff (indeed, any compact T1-space can occur as max A for some A), and min A is always Hausdorff (in fact zero-dimensional), but not always compact. (For more information on max A and min A, see Simmons[3].)

The flat topology on the minimal and maximal prime spectrum of a commutative ring

2019 ◽  
Vol 18 (06) ◽  
pp. 1950110
Author(s):  
Esmaeil Rostami ◽  
Masoumeh Hedayati ◽  
Nosratollah Shajareh Poursalavati
Keyword(s):  
Topological Space ◽  
Commutative Ring ◽  
Chain Condition ◽  
Commutative Rings ◽  
Topological Properties ◽  
Prime Spectrum ◽  
Compact Topological Space ◽  
Algebraic Properties ◽  
Ascending Chain Condition

In this paper, we investigate connections between some algebraic properties of commutative rings and topological properties of their minimal and maximal prime spectrum with respect to the flat topology. We show that for a commutative ring [Formula: see text], the ascending chain condition on principal annihilator ideals of [Formula: see text] holds if and only if [Formula: see text] is a Noetherian topological space as a subspace of [Formula: see text] with respect to the flat topology and we give a characterization for a topological space [Formula: see text] for which [Formula: see text] is a Noetherian topological space as a subspace of [Formula: see text] with respect to the flat topology. Also, we give a characterization for rings whose maximal prime spectrum is a compact topological space with respect to the flat topology. Some other results are obtained too.

Electron Microscopy of Nucleic Acids

1974 ◽  
Vol 32 ◽  
pp. 302-303
Author(s):  
Norman Davidson
Keyword(s):  
Electron Microscopy ◽  
Nucleic Acids ◽  
Basic Protein ◽  
Molecular Biologist ◽  
Topological Properties ◽  
Protein Film ◽  
Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

The Effect of Topological Properties on Duration Perception of Oddball Stimuli

2013 ◽  
Vol 45 (12) ◽  
pp. 1324-1333
Author(s):  
Baolin LI ◽  
Youguo CHEN ◽  
Xiangyong YUAN ◽  
Jackson Todd ◽  
Xiting HUANG
Keyword(s):  
Topological Properties

Molecular Topological Properties of Alkylating Agents Based Anticancer Drug Candidates Via Some Ve-degree Topological Indices

2020 ◽  
Vol 16 (2) ◽  
pp. 190-195 ◽  
Author(s):  
Süleyman Ediz ◽  
Murat Cancan
Keyword(s):  
Anticancer Drugs ◽  
Anticancer Drug ◽  
Alkylating Agents ◽  
Topological Indices ◽  
Pharmacological Properties ◽  
Topological Properties ◽  
Drug Candidates ◽  
New Drug ◽  
Atom Bond ◽  
Dual Target

Background: Reckoning molecular topological indices of drug structures gives the data about the underlying topology of these drug structures. Novel anticancer drugs have been leading by researchers to produce ideal drugs. Materials and Methods: Pharmacological properties of these new drug agents explored by utilizing simulation strategies. Topological indices additionally have been utilized to research pharmacological properties of some drug structures. Novel alkylating agents based anticancer drug candidates and ve-degree molecular topological indices have been introduced recently. Results and Conclusion: In this study we calculate ve-degree atom-bond connectivity, harmonic, geometric-arithmetic and sum-connectivity molecular topological indices for the newly defined alkylating agents based dual-target anticancer drug candidates.

SOME TOPOLOGICAL PROPERTIES OF HAMEL BASES

1994 ◽  
Vol 20 (2) ◽  
pp. 819
Author(s):  
Muthuvel
Keyword(s):  
Topological Properties

scholarly journals DNA thermodynamics shape chromosome organization and topology

2013 ◽  
Vol 41 (2) ◽  
pp. 548-553 ◽  
Author(s):  
Andrew A. Travers ◽  
Georgi Muskhelishvili
Keyword(s):  
Dna Sequence ◽  
Dna Sequences ◽  
Chromosome Organization ◽  
Topological Properties ◽  
Genetic Organization ◽  
And Topology ◽  
Dna Translocases

How much information is encoded in the DNA sequence of an organism? We argue that the informational, mechanical and topological properties of DNA are interdependent and act together to specify the primary characteristics of genetic organization and chromatin structures. Superhelicity generated in vivo, in part by the action of DNA translocases, can be transmitted to topologically sensitive regions encoded by less stable DNA sequences.

scholarly journals Effect of Deformation on Topological Properties of Cobalt Monosilicide

Crystals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Sergey Nikolaev ◽  
Dmitry Pshenay-Severin ◽  
Yuri Ivanov ◽  
Alexander Burkov
Keyword(s):  
Band Structure ◽  
Ab Initio Calculations ◽  
Topological Charge ◽  
External Stress ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Topological Properties ◽  
Uniaxial Deformation ◽  
Band Crossing ◽  
Topological Charges

Recently, it was shown that materials with certain crystal structures can exhibit multifold band crossings with large topological charges. CoSi is one such material that belongs to non-centrosymmetric space group P213 (#198) and posseses multifold band crossing points with a topological charge of 4. The change of crystal symmetry, e.g., by means of external stress, can lift the degeneracy and change its topological properties. In the present work, the influence of uniaxial deformation on the band structure and topological properties of CoSi is investigated on the base of ab initio calculations. The k·p Hamiltonian taking into account deformation is constructed on the base of symmetry consideration near the Γ and R points both with and without spin-orbit coupling. The transformation of multifold band crossings into nodes of other types with different topological charges, their shift both in energy and in reciprocal space and the tilt of dispersion around nodes are studied in detail depending on the direction of uniaxial deformation.

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