On Skew Armendariz of Laurent Series Type Rings

http://dergipark.gov.tr/journal/380/article/504548/file/610778/download

“…The subring of the skew triangular matrices with constant main diagonal is denoted by S (R, n, α); and the subring of the skew triangular matrices with constant diagonals is denoted by T (R, n, α). It is well-known that T (R, n, α We consider the following two subrings of S(R, n, α), as follow (see [6,Page 13]).…”

“…We consider the following two subrings of S(R, n, α), as follow (see [6,Page 13]).…”

On a generalization of NC-McCoy rings

“…Let R be a ring and σ denote an endomorphism of R with σ(1) = 1. In [4] the authors introduced skew triangular matrix ring as a set of all triangular matrices with addition point-wise and a new multiplication subject to the condition…”

“…Therefore, clearly one can see that T (R, n, σ) ∼ = R[x; σ]/(x n ) is the ideal generated by x n in R[x; σ]. we consider the following two subrings of S(R, n, σ), as follows (see [4]):…”

“…Hence, R is right J-McCoy.Let R be a ring and σ denote an endomorphism of R with σ(1) = 1. In[4] the authors introduced skew triangular matrix ring as a set of all triangular matrices with addition point-wise and a new multiplication subject to the condition E ij r = σ j−i E ij .So (a ij )(b ij ) = (c ij ), where c ij = a ij b ij + a i,i+1 σ(b i+1,j )+ ...+ a ij σ j−i (b jj ), for each i ≤ j and denoted it by T n…”