LOOP RINGS SATISFYING IDENTITIES OF BOL-MOUFANG TYPE

The existence of loop rings that are not associative but which satisfy the Moufang or Bol identities is well known. Here we complete work started 25 years ago by establishing the existence of loop rings that satisfy any identity of "Bol-Moufang" type (without being associative). As it turns out, with one exception, loop rings satisfying an identity of Bol Moufang type all satisfy a Moufang or Bol identity. We also highlight some similarities and differences in the consequences of several Bol-Moufang identities as they apply to loops and rings.