In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be extended to this new approach and the c...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

Ageing is a process of physical, psychological and social change in multi-dimensional aspects. In Ayurveda the human body has been described as living subject where wear tear continuous perpetual phenomenon. Regeneration degeneration go simultaneously right from neonatal life to young age growth development occurs, after wards this altered takes upper hand. Rasayana therapy helps combating majo...

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...

While the Glion Colloquia have brought together university leaders from throughout the world to share their perspectives on a comprehensive array of critical issues confronting higher education, perhaps none is more imperative to consider than the role of the research university in an innovation-driven society. Research universities both in the United States and around the world are the primary...

ii To my family Pappa, Mom, Bhai, Bhabhi and Vrusti iii Acknowledgements I would like to express my sincerest gratitude to my advisor, Dr. Venkat Krovi, for giving me an opportunity to work under him. He was not only my mentor but also a friend and on occasions, a guardian guiding me through whenever I needed the most. His excellence in the field and enthusiasm to work extended hours has always...

The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension such that every proper homomorphic image is a...

A key goal of mobile computing is untethering devices from wires, making them truly portable. While mobile devices can make use of wireless communication for network connectivity, they are still dependent on an electrical connection for continued operation. This need for tethering to available electricity significantly limits their range, usefulness, and manageability. Environmental energy harv...

It is well known [5], [1] that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It...

By recovering the pre-critical foundations of Immanuel Kant's political idealism, this article elucidates his fundamental concern with reorienting “point view” real princes and sovereigns to cause peace. I trace priority reading Pierre Bayle, whose skepticism illustrated that true nature rendered Saint-Pierre's ideal peace “not possible.” Beginning in 1756, Kant reframed perpetual as ultimate h...