Commutativity of rings satisfying certain polynomial identities

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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...

متن کامل

Commutativity for a Certain Class of Rings

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 کامل

How 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(...

متن کامل

On Derandomizing Tests for Certain Polynomial Identities

We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm. We then discuss its possible application to other tests.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of the Australian Mathematical Society

سال: 1991

ISSN: 0004-9727,1755-1633

DOI: 10.1017/s0004972700029464