We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

Jack Dongarra, University of Tennessee, USA Edited by: Kuan-Ching Li, Providence University, Taiwan; Ching-Hsien Hsu, Chung Hua University, Taiwan; Laurence Tianruo Yang, St. Francis Xavier University, Canada; Jack Dongarra, University of Tennessee, USA; and Hans Zima, University of Vienna, Austria 13-digit ISBN: 978-1-60566-661-7 1,093 pages; 2010 Copyright Price: US $555.00 (hardcover*) Perpe...

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

Solution to the optimal stopping problem V (x) = sup τ Eeg(x+Xτ ) is given, where X = {Xt}t≥0 is a Lévy process, τ is an arbitrary stopping time, δ ≥ 0 is a discount rate, and the reward function g takes the form gc(x) = (x−K) or gp(x) = (K−x) Results, interpreted as option prices of perpetual options in Bachelier’s model are expressed in terms of the distribution of the overall supremum in cas...

The problem of quantifying a design requirement for perpetual endurance of solar-powered unmanned aerial vehicles (UAVs) is treated. The design requirement is formulated as a threshold of the Power Ratio, a non-dimensional number that characterizes the ability of an aircraft to fly while solar-powered. This socalled Perpetuity Threshold is identified, derived and shown to be related to the dura...

Let A be a Banach algebra. Then A the second dual of A is a Banach algebra with first (second) Arens product. We study the Arens products of A(= (A∗∗)∗∗). We fined some conditions on A to be a left ideal in A. We fined the biggest two sided ideal I of A, in which I is a left (right) ideal of A∗∗.

We prove that the only proper right ideal of the universal enveloping algebra of a finite–dimensional central simple Lie triple system over a field of characteristic zero is its augmentation ideal.

In this paper, we introduce the concept of level sets of fuzzy HX left ideal and fuzzy HX right ideal of a HX ring . Also we have discussed the properties of fuzzy HX righ t(left) ideal under homomorphism and anti homomorphism by establishing the relationship among them.