A. M. Dhorajia

collaborators

3 papers

math.RA2017

Polynomial Rings Over Commutative Reduced Hopfian Local Rings

Alpesh M. Dhorajia, Himadri Mukherjee

In this paper we prove that if $R$ is a commutative, reduced, local ring, then $R$ is Hopfian if and only if the ring $R [x]$ is Hopfian. This answers a question of Varadarajan, in…

math.AC2010

A note on cancellation of projective modules

Alpesh M. Dhorajia, Manoj K. Keshari

Let $A$ be a ring of dimension $d$ . Assume that for every finite extension ring $R$ of $A$ , E_{d+1}(R) acts transitively on Um_{d+1}(R). Then we prove that E(A\oplus P) acts transi…

math.AC2010

Projective modules over overrings of polynomial rings

Alpesh M. Dhorajia, Manoj K. Keshari

Let A be a commutative Noetherian ring of dimension d and let P be a projective R=A[X_1,\ldots,X_l,Y_1,\ldots,Y_m,\frac {1}{f_1\ldots f_m}]-module of rank r\geq max {2,dim A+1, whe…