### SI-rings and their extensions as 2-primal rings

#### Abstract

Let R be a ring, σ an automorphism of R such that aσ(a) ∈ N(R) if and only if a ∈ N(R), where N(R) is the set of nilpotent elements of R and δ a σ-derivation of R such that δ(P) ⊆ P, for all minimal prime ideal P of R. We recall that a ring R is called an SI-ring if for a, b ∈ R, ab = 0 implies aRb = 0. In this paper we show that if R is a commutative Noetherian SI-ring, which is also an algebra over Q and σ and δ be as above, then R[x;σ,δ] is 2-primal.

**How to Cite this Article:**Smarti Gosani, V. K. Bhat, SI-rings and their extensions as 2-primal rings, J. Math. Comput. Sci., 7 (2017), 201-210 Copyright © 2017 Smarti Gosani, V. K. Bhat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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