Vol. 71, No. 2, 1977

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The maximal right quotient semigroup of a strong semilattice of semigroups

Antonio M. Lopez

Vol. 71 (1977), No. 2, 477–485

Let S be a strong semilattice Y of monoids. If S is right nonsingular then Y is nonsingular. The converse is true when S is a sturdy semilattice Y of right cancellative monoids. Should S have trivial multiplication then each monoid of more than one element has as its index an atom of Y . Finally, if S is a right nonsingular strong semilattice Y of principal right ideal Ore monoids with onto linking homomorphisms then Q(S), the maximal right quotient semigroup of S, is a semilattice Q(Y ) of groups.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 29 November 1976
Revised: 9 March 1977
Published: 1 August 1977
Antonio M. Lopez