S-sets and semigroups of quotients.
A subtraction semigroup is a semigroup with a further operation "" added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.
The semigroup of subspaces of the algebra of 2 × 2 matrices over a finite field is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.