When Is a Right Alternative Loop Ring That Is Also Right Bol Actually Moufang?

نویسندگان

  • ORIN CHEIN
  • MICHAEL KINYON
چکیده

In this paper, we consider some connections between loops whose loop rings, in characteristic 2, satisfy the Moufang identities and loops whose loop rings, in characteristic 2, satisfy the right Bol identities.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

3 0 Ju l 2 00 5 STRONGLY RIGHT ALTERNATIVE RINGS AND BOL LOOPS

We partially answer two questions of Goodaire by showing that in a finite, strongly right alternative ring, the set of units (if the ring is with unity) is a Bol loop under ring multiplication, and the set of quasiregular elements is a Bol loop under " circle " multiplication. A magma (L, ·) is a set L with a binary operation · : L × L → L. A magma (L, ·) is a loop if there is a neutral element...

متن کامل

On the Universality of Some Smarandache Loops of Bol-moufang Type

A Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, gprincipal isotopes. Conversely, it is shown that if these weak Smaranda...

متن کامل

A class of simple proper Bol loops ∗ Gábor

For a loop Q, we call the maps La(x) = ax,Ra(x) = xa left and right translations, respectively. These are permutations of Q, generating the left and right multiplication groups LMlt(Q),RMlt(Q) of Q, respectively. The group closure Mlt(Q) of LMlt(Q) and RMlt(Q) is the full multiplication group of Q. Just like for groups, normal subloops are kernels of homomorphisms of loops. The loop Q is simple...

متن کامل

Alternative Loop Rings

DRAFT Abstract The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.

متن کامل

Incidence Properties of Cosets in Loops

We study incidence properties among cosets of finite loops, with emphasis on well-structured varieties such as antiautomorphic loops and Bol loops. While cosets in groups are either disjoint or identical, we find that the incidence structure in general loops can be much richer. Every symmetric design, for example, can be realized as a canonical collection of cosets of a finite loop. We show tha...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008