Dual automorphism-invariant modules

A module $M$ is called an automorphism-invariant module if every isomorphism between two essential submodules of $M$ extends to an automorphism of $M$. This paper introduces the notion of dual of such modules. We call a module $M$ to be a dual automorphism-invariant module if whenever $K_1$ and $K_2$ are small submodules of $M$, then any epimorphism $\eta:M/K_1\rightarrow M/K_2$ with small kernel lifts to an endomorphism $\varphi$ of $M$. In this paper we give various examples of dual automorphism-invariant module and study its properties. In particular, we study abelian groups and prove that dual automorphism-invariant abelian groups must be reduced. It is shown that over a right perfect ring $R$, a lifting right $R$-module $M$ is dual automorphism-invariant if and only if $M$ is quasi-projective.Comment: To appear in Journal of Algebr

Rings of Invariant Module Type and Automorphism-Invariant Modules

A module is called automorphism-invariant if it is invariant under any automorphism of its injective hull. In [Algebras for which every indecomposable right module is invariant in its injective envelope, Pacific J. Math., vol. 31, no. 3 (1969), 655-658] Dickson and Fuller had shown that if $R$ is a finite-dimensional algebra over a field $\mathbb F$ with more than two elements then an indecomposable automorphism-invariant right $R$-module must be quasi-injective. In this paper we show that this result fails to hold if $\mathbb F$ is a field with two elements. Dickson and Fuller had further shown that if $R$ is a finite-dimensional algebra over a field $\mathbb F$ with more than two elements, then $R$ is of right invariant module type if and only if every indecomposable right $R$-module is automorphism-invariant. We extend the result of Dickson and Fuller to any right artinian ring. A ring $R$ is said to be of right automorphism-invariant type (in short, RAI-type) if every finitely generated indecomposable right $R$-module is automorphism-invariant. In this paper we completely characterize an indecomposable right artinian ring of RAI-type.Comment: To appear in Contemporary Mathematics, Amer. Math. So

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Some ratio type estimators under measurement errors

This article addresses the problem of estimating the population mean using auxiliary information in the presence of measurement errors

Ichthyofaunal diversity in Bachan Gad and Kakda streams of the Mid-himalayan Ganga river system of Garhwal in relation to stream gradient and distance

The present study was carried out to investigate the comparative seasonal distribution and relative abundance of fish fauna of streams Bachan Gad of river Alaknanda and Kakda Gad of river Mandakini of Mid-himalayan Ganga river System. Total length of the Bachan Gad is 14.5 km from origin to the confluence at main river Alaknanda with an altitudinal variation from 605.94 to 1418.23m (a.s.1), whereas, total length of the Kakda Gad is 15.5 km. from origin to confluence at main river Mandakini with altitudinal variation from 984.50 to 1993.70 m (a.s.1). Total 23 species from Bachan Gad and 20 fish species were identified from Kakda Gad. The differences in the availability of fish-fauna were directly related to the nature of the profile and slope of tributaries; which affects the migration and breeding grounds of the fishes inhabited in the main river Alaknanda and Mandakini of Ganga river system. Variation in the availability of fishes has been recorded from different sites of the stream. In streams and rivers the changes take place along their length is directly related to the eco-physico-chemical nature (water depth, current, substratum etc). All these factors which change along the length of streams are also the factors which control the distribution of the various sections of the biotic fauna and flora

Quantitative osteological study of a bottom feeder hillstream cyprinoid fish Crossocheilus latius latius (Hamilton- Buchanan)

The quantitative osteological study has been conducted on a Hillstream bottom feeder fish Crossocheilus latius latius. C. latius latius is a common hillstream fish of Snowfed Rivers of Alaknanda. The bones have been taken from different sized fishes ranged from 13 to 27 Cm in length and 39 to 132 gm in weight. The correlation is applied between Body Weight and the Weight of different disarticulated bones of C. latius latius. The correlation (r) is highly significant among the different parameter of body in relation to osteology which ranged from r = 0.952; P<0.1 to r = 0.999; P< 0.1

Nutrient Management for Higher Productivity of Swarna Sub1 Under Flash Floods Areas

Two field experiments were conducted at Regional Agricultural Research Station, Tarahara, Nepal during 2012 and 2013 to determine the effect of agronomic management on growth and yield of Swarna Sub1 under flash floods. The first experiment was laid out in a split plot design with three replications; and four different nutrient combinations at nursery as main plots and three age groups of rice seedlings as sub plots. The second experiment was laid out in a randomized complete block design and replicated thrice; with three post flood nutrient doses at six and 12 days after de-submergence (dad). The experiments were complete submerged at 10 days after transplanting for 12 days. The survival percentage, at 21 dad, was significantly higher in plots planted with 35 (90.25%) and 40 (91.58%) days-old seedlings compared to 30 days-old seedlings (81.75%). Plots with 35 days-old seedlings produced 5.15 t ha-1 with advantage of 18.83% over 30 days-old seedlings. Plots with 100-50-50 kg N-P2O5-K2O/ha at nursery recorded the highest grain filling of 79.41% and grain yield of 5.068 t/ha with more benefit. Post flood application of 20-20 N-K20kg/ha at 6 dad resulted in higher plant survival and taller plants, leading to significantly higher grain yield of 5.183 t/ha and straw yield of 5.315 t/ha. Hence, 35-40 days old seedlings raised with 100-50-50 kg N-P2O5-K2O /ha in nursery and the additional application of20-20 kg N-K2O /ha at 6 dad improved plant survival and enhanced yield of Swarna Sub1 under flash flood conditions. The practice has prospects of saving crop loss with getting rice yield above national average yield leading to enhanced food security in the flood prone areas of Nepal

Temperature dependence of 1/f noise in Gallium Nitride epitaxial layer

1/f noise investigation was performed on n-GaN epitaxial layer grown on sapphire. The variation of spectral power density of voltage fluctuations density was observed as a function of frequency (100-50 Hz) and it showed the 1/f spectra. This type of behavior was attributed to the presence of traps. The variation in spectral power density of voltage fluctuations with temperature was also observed with in the temperature range 80 K and 300 K and it was found to be slightly increasing with temperature. It was attributed to the trapping-detrapping process of charge carriers by the defects. Four probe configuration was used for noise measurement and contacts were made with indium. To check the stability and ohmic behavior of contacts, I-V measurements were performed with in the temperature range 80-325 K. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2201