Journal Title/Source

Journal of Algebra and its Applications

Publication Date

2014

Volume

13

Page Numbers

1-5

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

There are four standard Moufang identities; call them (M1),(M2),(M3), and (M4) (their definitions are given below). In the variety of loops they are equivalent; that is, each of these identities implies the other three. It was shown in [8] that magmas with inverses that satisfy either (M1) or (M2) are, in fact, loops, while magmas with inverses that satisfy either (M3) or (M4) need not be loops. We show here that 2-divisible magmas with inverses that satisfy either (M3) or (M4) are loops. We also establish all implications between (M1),(M2),(M3) and (M4) in the variety of magmas with inverses.

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