DRl-semigroups and MV-algebras
Jiří Rachůnek · Czechoslovak Mathematical Journal · 1998
The notion of a DRl-semigroup was introduced by K.L.N.Swamy in [7] as a common generalization of Brouwerian algebras and abelian lattice ordered groups (lgroups).A DRlsemigroup is an algebra A = (A, +, 0, ∨, ∧, -) of type 2, 0, 2, 2, 2 such that (1) (A, +, 0) is a commutative monoid, (2) (A, ∨, ∧) is a lattice, (3) (A, +, ∨, ∧) is a lattice ordered semigroup (l-semigroup), i.e.A satisfies the identities x + (y ∨ z) = (x + y) ∨ (x + z),x + (y ∧ z) = (x + y) ∧ (x + z).