Commutativity of rings satisfying certain polynomial identities
نویسندگان
چکیده
منابع مشابه
Some Polynomial Identities that Imply Commutativity of Rings
In this paper, we establish some commutativity theorems for certain rings with polynomial constraints as follows: Let R be an associative ring, and for all x, y ∈ R, and fixed non-negative integers m > 1, n ≥ 0, r > 0, s ≥ 0, t ≥ 0, p ≥ 0, q ≥ 0 such that P (x, y) = ±Q(x, y), where P (x, y) = ys[x, y]yt and Q(x, y) = xp[xm, yn]ryq. First,it is shown that a semiprime ring R is commutative if and...
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We discuss the commutativity of certain rings with unity 1 and one-sided s-unital rings under each of the following conditions: xr[xs, y] = ±[x, yt]xn, xr[xs, y] = ±xn[x, yt], xr[xs, y] = ±[x, yt]ym, and xr[xs, y] = ±ym[x, yt], where r, n, and m are non-negative integers and t > 1, s are positive integers such that either s, t are relatively prime or s[x, y] = 0 implies [x, y] = 0. Further, we ...
متن کاملHow much commutativity is needed to prove polynomial identities?
Let f be a non-commutative polynomial such that f = 0 if we assume that the variables in f commute. Let Q(f) be the smallest k such that there exist polynomials g1, g ′ 1, g2, g ′ 2, . . . , gk, g ′ k with f ∈ I([g1, g 1], [g2, g 2], . . . , [gk, g k]) , where [g, h] = gh − hg. Then Q(f) ≤ ` n 2 ́ , where n is the number of variables of f . We show that there exists a polynomial f with Q(f) = Ω(...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1991
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700029464