Experimenting with the Identity (xy)z = y(zx)
نویسندگان
چکیده
An experiment with the nonassociative algebra program Albert led to the discovery of the following surprising theorem. Let G be a groupoid satisfying the identity (xy)z = y(zx). Then for products in G involving at least ve elements, all factors commute and associate. A corollary is that any semiprime ring satisfying this identity must be commutative and associative, generalizing a known result of Chen.
منابع مشابه
Linear groupoids and the associated wreath products
A groupoid identity is said to be linear of length 2k if the same k variables appear on both sides of the identity exactly once. We classify and count all varieties of groupoids defined by a single linear identity. For k = 3, there are 14 nontrivial varieties and they are in the most general position with respect to inclusion. Hentzel et. al. [3] showed that the linear identity (xy)z = y(zx) im...
متن کاملDerivations of a Finite Dimensional Jb∗-triple (after Meyberg)
and [[xy]z] + [[yz]x] + [[zx]y] = 0. Left multiplication in a Lie algebra is denoted by ad(x): ad(x)(y) = [x, y]. An associative algebra A becomes a Lie algebra A− under the product, [xy] = xy − yx. The first axiom implies that [xy] = −[yx] and the second (called the Jacobi identity) implies that x 7→ adx is a homomorphism of L into the Lie algebra (EndL)−, that is, ad [xy] = [adx, ad y]. Assum...
متن کاملThe November Meeting in St, Louis
s of all papers presented at the meeting are given below. Papers read by title are indicated by the letter t" Paper number 48 was presented by Professor Chatland, number 54 by Mr. Block, number 58 by Professor Ulrich, number 72 by Mr. Kelly, and number 82 by Dr. Moise. ALGEBRA AND THEORY OF NUMBERS 47/. A. A. Albert: Power-associative rings. I I . A power-associative algebra A over a field F is...
متن کاملMixed Arithmetic and Geometric Means and Related Inequalities
Mixed arithmetic and geometric means, with and without weights, are both considered. Related to mixed arithmetic and geometric means, the following three types of inequalities and their generalizations, from three variables to a general n variables, are studied. For arbitrary x, y, z ≥ 0 we have [ x + y + z 3 (xyz) ]1/2 ≤ ( x + y 2 · y + z 2 · z + x 2 )1/3 , (A) 1 3 (√ xy + √ yz + √ zx ) ≤ 1 2 ...
متن کاملA generalization of entropy equation: homogeneous entropies
Shannon's entropy has been characterized in several ways. Kaminski and Mikusihski [5] simplified Fadeev's [3] approach by considering, what they called the entropy equation: (1.1) H(x, y, z) = H(x + y, 0, z) + H(x, y, 0) , (x ^ 0 , y ^ 0 , z > 0 , xy + yz + zx > 0) . A general continuous symmetric solution of (1.1) given by (1.2) H(x, y, z) = (x + y + z) log (x + y + z) — x log x y log y — z lo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 16 شماره
صفحات -
تاریخ انتشار 1993