2017/07/10 by Singh, Sushma, Prakash, Om
#16N40 #16S36 #16U99 #16W20 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1707.02820
A ring R is said to be an almost Armendariz ring if whenever product of two polynomials in R[x] is zero, then product of their coefficients are in N*(R). In this article, for an endomorphism α on R, we define an α-almost Armendariz ring of R considering the polynomials in skew polynomial ring R[x; α] instead of R[x]. It is the generalisation of an almost Armendariz ring [9] and an α-Armendariz ring [4]. Moreover, for an endomorphism α of R, we define an α-skew almost Armendariz ring, and prove that a reversible ring R with certain condition on endomorphism α, its polynomial ring R[x] is an α-skew almost Armendariz ring.