Document Details Document Type : Article In Journal  Document Title : Commutativity of rings with variable constraints Commutativity of rings with variable constraints   Document Language : Arabic  Abstract : Let m > 1, r greater than or equal to 0 be fixed non-negative integers and R a ring with unity 1 in which for each x is an element of R, there exists a polynomial f(X,Y) = f(x)(X,Y) in R(X, Y) satisfying the condition that for all y in R f(x, y) = f(x, y + 1) = f(x, x + y) so that either of the properties y(r)[x, y(m)] = f(x, y) or [x, y(m)]y(r) = f(x, y) for all y in R. The main result of the present paper asserts that R is commutative if it satisfies the property Q(m) (for all x, y is an element of R, m[x, y] = 0 implies [x, y] = 0). Finally, some results have been extended to one-sided s-unital rings.  Journal Name : PUBLICATIONES MATHEMATICAE-DEBRECEN  Volume : 58  Issue Number : 3  Publishing Year : 2001 AH   Added Date : Tuesday, June 24, 2008  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email Khan MA Khan MA Researcher     Back To Researches Page