E-resources
Peer reviewed
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Ebrahim Hashemi; Fatemeh Shokuhifar
Journal of the Korean Mathematical Society, 01/2019Journal Article
Let $R$ be a commutative ring with unity. In this paper, we characterize the unit elements, the regular elements, the $\pi$-regular elements and the clean elements of zero-symmetric near-ring of polynomials $R_{0}x$, when $ \mathrm{nil}(R)^{2}=0 $. Moreover, it is shown that the set of $\pi$-regular elements of $R_{0}x$ forms a semigroup. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its ``multiplication'' operation. KCI Citation Count: 2
