scholarly journals On prime essential rings

1993 ◽  
Vol 47 (2) ◽  
pp. 287-290 ◽  
Author(s):  
Halina France-Jackson
Keyword(s):  
Prime Ideal ◽  
Nonzero Ideal ◽  
Lower Radical ◽  
Semisimple Class ◽  
Open Questions ◽  
Nonzero Intersection

A ring A is prime essential if A is semiprime and every prime ideal of A has a nonzero intersection with each nonzero ideal of A. We prove that any radical (other than the Baer's lower radical) whose semisimple class contains all prime essential rings is not special. This yields non-speciality of certain known radicals and answers some open questions.

scholarly journals ON SUPERNILPOTENT NONSPECIAL RADICALS

2008 ◽  
Vol 78 (1) ◽  
pp. 107-110
Author(s):  
HALINA FRANCE-JACKSON
Keyword(s):  
Prime Ring ◽  
Jacobson Radical ◽  
Minimal Ideal ◽  
Negative Answer ◽  
Nonzero Ideal ◽  
Subdirectly Irreducible ◽  
Lower Radical ◽  
Simple Ring ◽  
Factor Ring ◽  
Semisimple Class

AbstractLet ρ be a supernilpotent radical. Let ρ* be the class of all rings A such that either A is a simple ring in ρ or the factor ring A/I is in ρ for every nonzero ideal I of A and every minimal ideal M of A is in ρ. Let $\mathcal {L}\left ( \rho ^{\ast }\right ) $ be the lower radical determined by ρ* and let ρφ denote the upper radical determined by the class of all subdirectly irreducible rings with ρ-semisimple hearts. Le Roux and Heyman proved that $\mathcal {L}\left ( \rho ^{\ast }\right ) $ is a supernilpotent radical with $\rho \subseteq \mathcal {L}\left ( \rho ^{\ast }\right ) \subseteq \rho _{\varphi }$ and they asked whether $\mathcal {L} \left ( \rho ^{\ast }\right ) =\rho _{\varphi }$ if ρ is replaced by β, ℒ , 𝒩 or 𝒥 , where β, ℒ , 𝒩 and 𝒥 denote the Baer, the Levitzki, the Koethe and the Jacobson radical, respectively. In the present paper we will give a negative answer to this question by showing that if ρ is a supernilpotent radical whose semisimple class contains a nonzero nonsimple * -ring without minimal ideals, then $\mathcal {L}\left ( \rho ^{\ast }\right ) $ is a nonspecial radical and consequently $\mathcal {L}\left ( \rho ^{\ast }\right ) \neq \rho _{\varphi }$. We recall that a prime ring A is a * -ring if A/I is in β for every $0\neq I\vartriangleleft A$.

On the number of incongruent solutions to a quadratic congruence over algebraic integers

2019 ◽  
Vol 15 (01) ◽  
pp. 105-130
Author(s):  
Ramy F. Taki Eldin
Keyword(s):  
Prime Ideal ◽  
Number Field ◽  
Exponential Sums ◽  
Nonzero Ideal ◽  
Explicit Formulas ◽  
Algebraic Integers ◽  
Ideal Formula ◽  
Quadratic Congruence ◽  
Ring Of Algebraic Integers

Over the ring of algebraic integers [Formula: see text] of a number field [Formula: see text], the quadratic congruence [Formula: see text] modulo a nonzero ideal [Formula: see text] is considered. We prove explicit formulas for [Formula: see text] and [Formula: see text], the number of incongruent solutions [Formula: see text] and the number of incongruent solutions [Formula: see text] with [Formula: see text] coprime to [Formula: see text], respectively. If [Formula: see text] is contained in a prime ideal [Formula: see text] containing the rational prime [Formula: see text], it is assumed that [Formula: see text] is unramified over [Formula: see text]. Moreover, some interesting identities for exponential sums are proved.

scholarly journals ON SUPERNILPOTENT RADICALS WITH THE AMITSUR PROPERTY

2009 ◽  
Vol 80 (3) ◽  
pp. 423-429 ◽  
Author(s):  
HALINA FRANCE-JACKSON
Keyword(s):  
Jacobson Radical ◽  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Prime Radical ◽  
Factor Ring ◽  
Semisimple Class ◽  
Primitive Ring

AbstractA radical α has the Amitsur property if α(A[x])=(α(A[x])∩A)[x] for all rings A. For rings R⊆S with the same unity, we call S a finite centralizing extension of R if there exist b1,b2,…,bt∈S such that S=b1R+b2R+⋯+btR and bir=rbi for all r∈R and i=1,2,…,t. A radical α is FCE-friendly if α(S)∩R⊆α(R) for any finite centralizing extension S of a ring R. We show that if α is a supernilpotent radical whose semisimple class contains the ring ℤ of all integers and α is FCE-friendly, then α has the Amitsur property. In this way the Amitsur property of many well-known radicals such as the prime radical, the Jacobson radical, the Brown–McCoy radical, the antisimple radical and the Behrens radical can be established. Moreover, applying this condition, we will show that the upper radical 𝒰(*k) generated by the essential cover *k of the class * of all *-rings has the Amitsur property and 𝒰(*k)(A[x])=𝒰(*k)(A)[x], where a semiprime ring R is called a *-ring if the factor ring R/I is prime radical for every nonzero ideal I of R. The importance of *-rings stems from the fact that a *-ring A is Jacobson semisimple if and only if A is a primitive ring.

A PRIME ESSENTIAL RING THAT GENERATES A SPECIAL ATOM

2016 ◽  
Vol 95 (2) ◽  
pp. 214-218
Author(s):  
SRI WAHYUNI ◽  
INDAH EMILIA WIJAYANTI ◽  
HALINA FRANCE-JACKSON
Keyword(s):  
Prime Ideal ◽  
Semiprime Ring ◽  
Minimal Element ◽  
Special Radical ◽  
Nonzero Intersection

A special atom (respectively, supernilpotent atom) is a minimal element of the lattice $\mathbb{S}$ of all special radicals (respectively, a minimal element of the lattice $\mathbb{K}$ of all supernilpotent radicals). A semiprime ring $R$ is called prime essential if every nonzero prime ideal of $R$ has a nonzero intersection with each nonzero two-sided ideal of $R$. We construct a prime essential ring $R$ such that the smallest supernilpotent radical containing $R$ is not a supernilpotent atom but where the smallest special radical containing $R$ is a special atom. This answers a question put by Puczylowski and Roszkowska.

RADICAL RELATED TO SPECIAL ATOMS REVISITED

2014 ◽  
Vol 91 (2) ◽  
pp. 202-210
Author(s):  
HALINA FRANCE-JACKSON ◽  
SRI WAHYUNI ◽  
INDAH EMILIA WIJAYANTI
Keyword(s):  
Semiprime Ring ◽  
Nonzero Ideal ◽  
Prime Radical ◽  
Radical Theory ◽  
Factor Ring ◽  
Open Questions ◽  
Open Question ◽  
The Way

AbstractA semiprime ring $R$ is called a $\ast$-ring if the factor ring $R/I$ is in the prime radical for every nonzero ideal $I$ of $R$. A long-standing open question posed by Gardner asks whether the prime radical coincides with the upper radical $U(\ast _{k})$ generated by the essential cover of the class of all $\ast$-rings. This question is related to many other open questions in radical theory which makes studying properties of $U(\ast _{k})$ worthwhile. We show that $U(\ast _{k})$ is an N-radical and that it coincides with the prime radical if and only if it is complemented in the lattice $\mathbb{L}_{N}$ of all N-radicals. Along the way, we show how to establish left hereditariness and left strongness of important upper radicals and give a complete description of all the complemented elements in $\mathbb{L}_{N}$.

What’s Next?

2011 ◽  
Vol 23 (1) ◽  
pp. 60-63 ◽  
Author(s):  
Peter Vorderer
Keyword(s):  
Cultural Differences ◽  
Factor Model ◽  
New Developments ◽  
Theoretical Concepts ◽  
Open Questions ◽  
Entertainment Products ◽  
Entertainment Theory

This paper points to new developments in the context of entertainment theory. Starting from a background of well-established theories that have been proposed and elaborated mainly by Zillmann and his collaborators since the 1980s, a new two-factor model of entertainment is introduced. This model encompasses “enjoyment” and “appreciation” as two independent factors. In addition, several open questions regarding cultural differences in humans’ responses to entertainment products or the usefulness of various theoretical concepts like “presence,” “identification,” or “transportation” are also discussed. Finally, the question of why media users are seeking entertainment is brought to the forefront, and a possibly relevant need such as the “search for meaningfulness” is mentioned as a possible major candidate for such an explanation.

Dose Tracker Application for Collecting Medication Use Data from International Space Station Crew

2020 ◽  
Vol 91 (1) ◽  
pp. 41-45 ◽  
Author(s):  
Virginia. E. Wotring ◽  
LaRona K. Smith
Keyword(s):  
Data Collection ◽  
International Space Station ◽  
Sleep Disturbances ◽  
Space Station ◽  
Medication Use ◽  
International Space ◽  
Flight Data ◽  
Open Questions ◽  
Share Data ◽  
Usability Feedback

INTRODUCTION: There are knowledge gaps in spaceflight pharmacology with insufficient in-flight data to inform future planning. This effort directly addressed in-mission medication use and also informed open questions regarding spaceflight-associated changes in pharmacokinetics (PK) and/or pharmacodynamics (PD).METHODS: An iOS application was designed to collect medication use information relevant for research from volunteer astronaut crewmembers: medication name, dose, dosing frequency, indication, perceived efficacy, and side effects. Leveraging the limited medication choices aboard allowed a streamlined questionnaire. There were 24 subjects approved for participation.RESULTS: Six crewmembers completed flight data collection and five completed ground data collection before NASA’s early study discontinuation. There were 5766 medication use entries, averaging 20.6 ± 8.4 entries per subject per flight week. Types of medications and their indications were similar to previous reports, with sleep disturbances and muscle/joint pain as primary drivers. Two subjects treated prolonged skin problems. Subjects also used the application in unanticipated ways: to note drug tolerance testing or medication holiday per research protocols, and to share data with flight surgeons. Subjects also provided usability feedback on application design and implementation.DISCUSSION: The volume of data collected (20.6 ± 8.4 entries per subject per flight week) is much greater than was collected previously (<12 per person per entire mission), despite user criticisms regarding app usability. It seems likely that improvements in a software-based questionnaire application could result in a robust data collection tool that astronauts find more acceptable, while simultaneously providing researchers and clinicians with useful data.Wotring VE, Smith LK. Dose tracker application for collecting medication use data from International Space Station crew. Aerosp Med Hum Perform. 2020; 91(1):41–45.

DAMPAK PROGRAM DIKLAT ONLINE TIK GURU PUSTEKKOM TERHADAP AKSESBILITAS KONTEN PEMBELAJARAN PADA FITUR RUMAH BELAJAR

2018 ◽  
Vol 19 (2) ◽  
pp. 84
Author(s):  
Eni Susilawati
Keyword(s):  
Teacher Training ◽  
Quantitative Research ◽  
Online Training ◽  
Research Approach ◽  
Intensity Level ◽  
Web Based ◽  
Learning Content ◽  
Open Questions ◽  
Ict Training ◽  
The Impact

The research objective is to analyze the impact of the participation of online  ICT teacher training to increase the number of accessibility the learning content of features in Rumah Belajar. This research used the quantitative research approach with descriptive quantitative analysis methods to be able to describe how the increase in accessibility features of Rumah Belajar and utilization in learning in school. Samples were selected in this study are all online training participants at 15 locations online training that has been conducted by Pustekkom in 2015 and 2016 in 2015. The data was collected using a questionnaire and a list of open questions in accordance with the purpose of research. The results showed that 1) online ICT teacher training participants, after completing the Pustekkom  training online  using become more motivated to access other feature in Rumah Belajar; 2) The order of the percentage of the intensity level of accessibility to the other features of Rumah Belajar are: Sumber Belajar 23%, BSE 23%, Bank Soal 21%, Kelas Maya 13%, Lab Maya 6%, Karya Guru 4%, Wahana Jelajah Angkasa 4%, Peta Budaya 4% and Karya Komunitas 2%, and ICT training online using the application PKB Rumah Belajar can be used as a reference for efforts to develop a web-based learning applications, in particular for the development of Rumah belajar portal belongs Pustekkom Kemendikbud. Tujuan penelitian yaitu untuk menganalisis dampak keikutsertaan diklat online  TIK guru Belajar terhadap peningkatan jumlah aksebilitas konten pembelajaran pada fitur-fitur rumah belajar. Penelitian ini menggunakan pendekatan penelitian kuantitatif dengan metode analisis kuantitatif secara deskriptif untuk bisa menggambarkan bagaimana peningkatan aksesbilitas fitur-fitur rumah belajar dan pemanfaatannya dalam pembelajaran di sekolah. Sampel yang dipilih dalam penelitian ini adalah semua peserta diklat online  pada 15 lokasi diklat online yang telah dilaksanakan oleh Pustekkom pada tahun 2015 dan 2016. Pengumpulan data menggunakan kuesioner dan daftar pertanyaan terbuka sesuai dengan tujuan penelitian. Hasil penelitian menunjukkan bahwa 1) peserta diklat online TIK Guru, setelah mengikuti diklat online Pustekkom, menjadi lebih termotivasi untuk mengakses fitur-fitur lainnya dalam Rumah Belajar; 2) Urutan prosentase tingkat intensitas aksesbilitas terhadap fitur-fitur Rumbel selain Pengembangan Keprofesian berkelanjutan (PKB) adalah: Sumber Belajar 23%, Buku Sekolah Elektronik (BSE) 23%, Bank Soal 21%, Kelas Maya 13%, Lab Maya 6%, Karya Guru 4%, Wahana Jelajah Angkasa 4%, Peta Budaya 4% dan Karya Komunitas 2%; dan 3) diklat online TIK menggunakan aplikasi PKB. Rumah belajar bisa dijadikan referensi bagi upaya pengembangan aplikasi pembelajaran berbasis web, khususnya bagi pengembangan portal Rumah Belajar milik Pustekkom Kemendikbud.

Revisiting the High-Pressure Properties of the Metal-Organic Frameworks ZIF-8 and ZIF-67

2020 ◽  
Author(s):  
Pia Vervoorts ◽  
Stefan Burger ◽  
Karina Hemmer ◽  
Gregor Kieslich
Keyword(s):  
High Pressure ◽  
State Of The Art ◽  
Energy Landscape ◽  
Structural Flexibility ◽  
Zeolitic Imidazolate Frameworks ◽  
Stimuli Responsive ◽  
X Ray Diffraction ◽  
X Ray ◽  
Open Questions ◽  
Metal Organic

The zeolitic imidazolate frameworks ZIF-8 and ZIF-67 harbour a series of fascinating stimuli responsive properties. Looking at their responsitivity to hydrostatic pressure as stimulus, open questions exist regarding the isotropic compression with non-penetrating pressure transmitting media. By applying a state-of-the-art high-pressure powder X-ray diffraction setup, we revisit the high-pressure behaviour of ZIF-8 and ZIF-67 up to <i>p</i> = 0.4 GPa in small pressure increments. We observe a drastic, reversible change of high-pressure powder X-ray diffraction data at <i>p</i> = 0.3 GPa, discovering large volume structural flexibility in ZIF-8 and ZIF-67. Our results imply a shallow underlying energy landscape in ZIF-8 and ZIF-67, an observation that might point at rich polymorphism of ZIF-8 and ZIF-67, similar to ZIF-4(Zn).<br>

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