5 papers
Modules in which pure submodule is essential in a direct summand
Kaushal Gupta, Shiv Kumar, Ashok Ji Gupta
In this paper, we study the class of modules have the property that every pure submodule is essential in a direct summand. These modules are termed as pure extending modules which…
Σ-dual Rickart modules
Shiv Kumar, Ashok Ji Gupta
In this paper, we dualize the concept of Σ-Rickart modules as Σ-dual Rickart modules. An R-module M is said to be Σ-dual Rickart if the direct sum of arbitrary copies of M is dual…
Connection between commutative algebra and topology
Sumit Kumar Upadhyay, Shiv Datt Kumar, Raja Sridharan
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
Existence of a Unique group of finite order
Sumit Kumar Upadhyay, Shiv Datt Kumar
Let be a positive integer. Then cyclic group of order is the only group of order iff g.c.d. , where denotes the Euler-phi function. In this articl…
Public Key Protocol Based on Amalgamated Free Product
Sumit Kumar Upadhyay, Shiv Datt Kumar, Ramji Lal
In the spirit of Diffie Hellman the concept of a protocol algebra is introduced using certain amalgamated free product of Braid group B and Thompson group T together with a nilpote…