대한수학회지 (Journal of the Korean Mathematical Society)

  • 제56권1호
  • /
  • Pages.183-195
  • /
  • 2019
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON SOME TYPE ELEMENTS OF ZERO-SYMMETRIC NEAR-RING OF POLYNOMIALS

  • Hashemi, Ebrahim (Faculty of Mathematical Sciences Shahrood University of Technology) ;
  • Shokuhifar, Fatemeh (Faculty of Mathematical Sciences Shahrood University of Technology)
  • 투고 : 2018.02.24
  • 심사 : 2018.07.16
  • 발행 : 2019.01.01
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초록

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.

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참고문헌

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