Book chapters will be unavailable on Saturday 24th August between 8am-12pm BST. This is for essential maintenance which will provide improved performance going forwards. Please accept our apologies for any inconvenience caused.
Let I be a set and let (I) denote the set consisting of the 0 matrix over I × I and the matrix units over I × I. Then for x, z in (I) and x≠0≠z, xyz≠0 has precisely one solution y. This and several other statements are shown to be equivalent characterizations of (I) regarded as a semigroup with zero.
1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.