Geodesic
Decreasing Baer semigroups
Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 46-51

Voir la notice de l'article provenant de la source Cambridge University Press

In [8] and [9] we initiated a study of lattice theory by means of Baer semigroups. Basically, a Baer semigroup is a multiplicative semigroup with 0 in which the left annihilator L(x) of each element x is a principal left ideal generated by an idempotent, while its right annihilator R(x) is a principal right ideal generated by an idempotent. By [8, Lemma 2, p. 86], L(0) has a unique idempotent generator 1 which is effective as a two-sided multiplicative identity for S. For any Baer semigroup S, if we use set inclusion to partially order both L = L (S) = {L(x) | x ∈ S} and R = R (S) = {R(x) | x ∈ S}, we have by [8, Theorem 5, p. 86], that L and R form dual isomorphic lattices with 0 and 1. The Baer semigroup S is said to coordinatize the lattice L in case L(S) is isomorphic to L. In connection with this, it is important to note that by [9, Theorem 2.3, p. 1214], a poset P with 0 and 1 is a lattice if and only if it can be coordinatized by a Baer semigroup. 
Janowitz, M. F. Decreasing Baer semigroups. Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 46-51. doi: 10.1017/S0017089500000513
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