Representation of Lattice Ordered Autometrized Algebras by Sheaves
B. V. Subba Rao · Institutional Repositories DataBase (IRDB) · 1980
Introduction.In [4] we have introduced the concept of a representable autometrized algebra A= (A,+, $, *) which includes commutative DRl-semigroups and hence commutative l-groups, Boolean algebras and Brouwerian algebras as special cases and proved that a lattice ordered autometrized algebra A= (A, +, $, *) is a subdirect product of totally ordered representable autometrized algebras if and only if A is representable and {a * (a u b)} n {b * (au b)} = 0 for all a, b in A. In [5] we have studied the geometry of a special class of representable autometrized algebras A = (A, +, $, *) satisfying (Rl) a * (an b) + an b = a for all a, b in A, and (R2) {a * (au b)} n {b * (a u b)} = 0 for all a, b in A, which is still wider than the class of commutative DRl-semigroups satisfying "(a-b)n(b-a) ~ 0 for all a, b in A".In [6], we have observed that the lattice of all congruence relations on a representable autometrized algebra A= (A,+, $, *) satisfying (Rl) is a distributive lattice and