Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS

  • Mohammadi, Rasul (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University) ;
  • Moussavi, Ahmad (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University) ;
  • Zahiri, Masoome (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
  • Received : 2015.02.22
  • Published : 2016.03.01
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Abstract

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

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References

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