Indian Journal of Science and Technology

Abstract

Objective: To generalize the a-skew McCoy rings. Methods: For a ring endomorphism a, we call a ring R Central a-skew McCoy if for each pair of nonzero polynomials f x a xi i i n ( ) =∑ =0 and g x b x R x j j j m ( ) = ∈ [ ; ] ∑ =0 a satisfy f(x)g(x) = 0, then there exists a nonzero element r Œ R with ai ai (r) ∈ C(R). Findings: For a ring R, we show that if a(e) = e for each idempotent e Œ R, then R is Central a-skew McCoy if and only if eR is Central a-skew McCoy if and only if (1 – e)R is Central a-skew McCoy. Also, we prove that if at = I R for some positive integer t, R is Central a-skew McCoy if and only if the polynomial ring R[x] is Central a-skew McCoy if and only if the Laurent polynomial ring R[x, x–1] is Central a-skew McCoy. Moreover, we give some examples to show that if R is Central a-skew McCoy, then Tn (R) is not necessary Central a-skew McCoy, but Dn (R) and Vn (R) are Central a-skew McCoy, where Dn (R) and Vn (R) are the subrings of the triangular matrices with constant main diagonal and constant main diagonals, respectively. 

Keywords: Central a-skew McCoy Ring, McCoy Ring, Ore Extension,-skew McCoy ring, ‎ Triangular Matrix Ring, Skew Polynomial Ring