scholarly journals Note on P.P. Rings: (A Supplement to Hattori’s Paper)

1960 ◽  
Vol 17 ◽  
pp. 167-170 ◽  
Author(s):  
Shizuo Endo
Keyword(s):  
Left Ideal ◽  
Short Note ◽  
Torsion Theory ◽  
Left And Right

A ring R is called, according to [2], a left p.p. ring if any principal left ideal of R is projective. A ring which is left and right p.p. is called a p.p. ring.In this short note we shall give some additional remarks to A. Hattori [2]. In Proposition 1 we shall give a characterization of commutative p.p. rings, and in Proposition 3 we shall give a generalization of Proposition 17 and 18 in [2], which shows also that the modified torsion theory over commutative p.p. rings coincides with the usual torsion theory.

scholarly journals On strong CNZ rings and their extensions

2020 ◽  
Vol 9 (2) ◽  
pp. 80-92
Author(s):  
Chenar Abdul Kareem Ahmed
Keyword(s):  
Nilpotent Elements ◽  
Left And Right

T.K. Kwak and Y. Lee called a ring R satisfy the commutativity of nilpotent elements at zero[1] if ab = 0 for a, b ∈ N(R) implies ba = 0. For simplicity, a ring R is called CNZ if it satisfies the commutativity of nilpotent elements at zero. In this paper we study an extension of a CNZ ring with its endomorphism. An endomorphism α of a ring R is called strong right ( resp., left) CNZ if whenever aα(b) = 0(resp., α(a)b = 0 ) for a, b ∈ N(R) ba = 0. A ring R is called strong right (resp., left) α-CNZ if there exists a strong right (resp., left) CNZ endomorphism α of R, and the ring R is called strong α- CNZ if R is both strong left and right α- CNZ. Characterization of strong α- CNZ rings and their related properties including extensions are investigated . In particular, it’s shown that a ring R is reduced if and only if U2(R) is a CNZ ring. Furthermore extensions of strong α- CNZ rings are studied.

scholarly journals A Note on Amenability of Locally Compact Quantum Groups

2014 ◽  
Vol 57 (2) ◽  
pp. 424-430 ◽  
Author(s):  
Piotr M. Sołtan ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Short Note ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups

AbstractIn this short note we introduce a notion called quantum injectivity of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. In particular, this provides a new characterization of amenability of locally compact groups.

scholarly journals Characterization of the IS200/IS605 Insertion Sequence Family in Halanaerobium Hydrogeniformans

Genes ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 484
Author(s):  
Michael Sadler ◽  
Melanie R. Mormile ◽  
Ronald L. Frank
Keyword(s):  
Insertion Sequence ◽  
Open Reading Frames ◽  
Insertion Sequences ◽  
Genome Plasticity ◽  
Mobile Dna ◽  
Dna Elements ◽  
Left And Right ◽  
Evolutionary Role ◽  
Reading Frames

Mobile DNA elements play a significant evolutionary role by promoting genome plasticity. Insertion sequences are the smallest prokaryotic transposable elements. They are highly diverse elements, and the ability to accurately identify, annotate, and infer the full genomic impact of insertion sequences is lacking. Halanaerobium hydrogeniformans is a haloalkaliphilic bacterium with an abnormally high number of insertion sequences. One family, IS200/IS605, showed several interesting features distinct from other elements in this genome. Twenty-three loci harbor elements of this family in varying stages of decay, from nearly intact to an ends-only sequence. The loci were characterized with respect to two divergent open reading frames (ORF), tnpA and tnpB, and left and right ends of the elements. The tnpB ORF contains two nearly identical insert sequences that suggest recombination between tnpB ORF is occurring. From these results, insertion sequence activity can be inferred, including transposition capability and element interaction.

On an elementary characterization of the increasing convex ordering, by an application

1994 ◽  
Vol 31 (3) ◽  
pp. 834-840 ◽  
Author(s):  
Armand M. Makowski
Keyword(s):  
Short Proof ◽  
Probability Distributions ◽  
Short Note ◽  
Comparison Result ◽  
Convex Ordering ◽  
Simple Characterization ◽  
Increasing Convex Ordering ◽  
Elementary Characterization

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

scholarly journals Two-sided localization in semiprime FBN rings

1984 ◽  
Vol 30 (2) ◽  
pp. 179-191
Author(s):  
M. H. Upham
Keyword(s):  
Torsion Theory ◽  
Prime Ideals ◽  
Closed Set ◽  
Left And Right ◽  
Torsion Theories ◽  
Quotient Rings

The main result of this paper is that the left- and right-quotient rings at a hereditary link closed set of prime ideals of a semiprime fully bounded Noetherian (FBN) ring coincide. This was a result already known for nonsemiprime FBN rigns, but a question left open in the semiprime case. A cornerstone of our approach is that the torsion theory determined by a link-closed hereditary set of prime ideals in an FBN ring is “nice”, but not necessarily perfect. Some conditions which do produce perfect torsion theories are investigated.

scholarly journals Short Note: Development and characterization of 16 new polymorphic microsatellite loci for Schima superba (Theaceae)

2013 ◽  
Vol 62 (1-6) ◽  
pp. 124-126 ◽  
Author(s):  
Hong-Yu Niu ◽  
Wan-Hui Ye ◽  
Zheng-Feng Wang ◽  
Ying Chen ◽  
Hong-Lin Cao ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Large Scale ◽  
Short Note ◽  
Schima Superba ◽  
Broad Leaved Forest ◽  
Genetic Diversity And Structure ◽  
Scale Structures ◽  
Polymorphic Microsatellite ◽  
Leaved Forest

Abstract Schima superba is a common dominant tree species in evergreen broad-leaved forest in subtropical China. Despite its multiple usages in wood industry, reforestation and traditional Chinese medicine, its genetic diversity is poorly studied. To help studying its genetic diversity and structure in the future, after microsatellite enrichment and screening, we identified 16 microsatellites in S. superba. These markers showed polymorphism in three populations. The number of alleles per locus ranged from 3 to 32 with a mean of 14. Within populations, the observed and unbiased expected heterozygosities ranged from 0.048 to 0.926 and from 0.048 to 0.949, respectively. The newly developed 16 microsatellites will be useful for investigating the genetic diversity and structure from large scale patterns to fine-scale structures in this species.

scholarly journals A 4-Year-Old Boy with Beckwith Wiedemann Syndrome (BWS)

PRILOZI ◽  
2018 ◽  
Vol 39 (2-3) ◽  
pp. 131-135
Author(s):  
Aleksandra Janchevska ◽  
Velibor Tasic ◽  
Nevenka Laban ◽  
Momir Polenakovic ◽  
Zoran Gucev ◽  
...  
Keyword(s):  
Clinical Presentation ◽  
Molecular Genetic ◽  
Methylation Pattern ◽  
Molecular Genetic Analysis ◽  
Differentially Methylated Region ◽  
Embryonal Tumors ◽  
Left And Right ◽  
Imprinting Control Region ◽  
Chromosome 11P15.5

Abstract Objectives: Molecular characterization of a patient with BWS. Clinical presentation and intervention: A 4-year-old boy with overgrowth (weight above 99th and height at 99th percentile) had longitudinal hemihypertrophy of the tongue and left cheek. In addition, there was a difference of one centimeter in the circumference of the left and right leg. Molecular genetic analysis revealed hypomethylation of KvDRM1 (LIT1) in the imprinting control region-2 (ICR2) on chromosome 11p15.5 and a normal methylation pattern of the H19-differentially methylated region (H19-DMR) in the ICR1. The estimated tumor risk was 1-5%. Conclusion: This patient with clinical characteristics of BWS has an imprinting defect associated with a low risk of embryonal tumors.

scholarly journals Short Note: Isolation and Characterization of 12 Polymorphic Microsatellite Markers in Engelhardia roxburghiana (Juglandaceae)

2014 ◽  
Vol 63 (1-6) ◽  
pp. 109-112 ◽  
Author(s):  
Dan-Dan Zhang ◽  
Pi Luo ◽  
Ying Chen ◽  
Zheng-Feng Wang ◽  
Wan-Hui Ye ◽  
...  
Keyword(s):  
Genetic Diversity ◽  
Microsatellite Markers ◽  
Short Note ◽  
Screening Method ◽  
Wide Distribution ◽  
Enriched Library ◽  
Isolation And Characterization ◽  
Nuclear Microsatellite ◽  
Polymorphic Microsatellite

Abstract Engelhardia roxburghiana is a common half evergreen tree with a wide distribution in southeast Asia. Despite its ecological and pharmaceutical values, its genetic diversity is poorly studied. Our objective was to develop nuclear microsatellite markers to investigate the level of genetic diversity within and among populations in the future. Using the microsatellite-enriched library and PCR-based screening method, 12 microsatellite markers were developed and showed polymorphism in a population. The number of alleles per locus for these 12 microsatellites ranged from four to 15. The observed and expected heterozygosities ranged from 0.358 to 0.897 and from 0.369 to 0.886, respectively. The developed microsatellites will be useful for studying genetic diversity and population structure in E. roxburghiana.

On an elementary characterization of the increasing convex ordering, by an application

1994 ◽  
Vol 31 (03) ◽  
pp. 834-840
Author(s):  
Armand M. Makowski
Keyword(s):  
Short Proof ◽  
Probability Distributions ◽  
Short Note ◽  
Comparison Result ◽  
Convex Ordering ◽  
Simple Characterization ◽  
Increasing Convex Ordering ◽  
Elementary Characterization

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

scholarly journals QF-3 rings and torsion theories

1989 ◽  
Vol 46 (2) ◽  
pp. 251-261 ◽  
Author(s):  
José L. Gómez Pardo ◽  
Nieves Rodríguez González
Keyword(s):  
Chain Condition ◽  
Torsion Theory ◽  
Additional Hypothesis ◽  
Left And Right ◽  
Torsion Theories ◽  
Torsion Radical ◽  
Ascending Chain Condition

AbstractIn this paper, the rings which have a torsion theory τ with associated torsion radical τ such that R/t(R) has a minimal τ-torsionfree cogenerator are studied. When τ is the trivial torsion theory these are precisely the left QF-3 rings. For τ = τL, the Lambek torsion theory, this class of rings is wider but, with an additional hypothesis on τL it is shown that if R has this property with respect to the Lambek torsion theory on both sides, then R is a (left and right) QF-3 ring. The results obtained are applied to get new characterizations of QF-3 rings with the ascending chain condition on left annihilators.

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