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Let A be a ring of dimension d and let P be a projective A-module of rank d. Assume that if R is a finite extension of A then R is cancellative. Then it is proved in ([10], Theorem 3.6) that P is… (More)

Let A be a commutative Noetherian ring of dimension d and let P be a projective R = A[X1, . . . , Xl, Y1, . . . , Ym, 1 f1...fm ]-module of rank r ≥ max {2, dimA+ 1}, where fi ∈ A[Yi]. Then (i)… (More)

Abstract: 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 1.1, in the case… (More)

- Alpesh M. Dhorajia, Jimmy M. Morzaria
- Discrete Math., Alg. and Appl.
- 2016

Let R be a commutative ring and Z(R) be its set of zero divisors. The total graph of R (introduced by Anderson and Badawi) denoted by TΓ (R). For any positive integers n and m we obtain the… (More)

- Alpesh M. Dhorajia
- Discrete Math., Alg. and Appl.
- 2015

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