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ON SOME TYPE ELEMENTS OF ZERO-SYMMETRIC NEAR-RING OF POLYNOMIALS

Hashemi, Ebrahim;Shokuhifar, Fatemeh

  • Received : 2018.02.24
  • Accepted : 2018.07.16
  • Published : 2019.01.01

Abstract

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 $nil(R)^2=0$. 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.

Keywords

near-ring of polynomials;regular elements;unit elements;${\pi}$-regular elements;clean elements