On Semilattices of Archimedean Semigroups — A Survey

The binary quasiorder on semigroups

“…Proposition 3.1 implies that is a semilattice congruence on X. The intersection of all semilattice congruences on a semigroup X is a semilattice congruence called the least semilattice congruence, denoted by η in [11], [12] (by ξ in [27], [14], and by ρ 0 in [6]). The minimality of η implies that η ⊆ .…”

“…This fundamental decomposition result was proved by Tamura [24] (see also [20], [21], [25]). Because of its fundamental importance, the least semilattice congruence has been deeply studied by many mathematicians, see the papers [7], [8], [9], [10], [13], [15], [16], [17], [18], [19], [20], [21], [23], [26], [27], [28], and monographs [6], [15], [22]. Nonetheless, some important facts about the semilattice decompositions of Ecentral semigroups seem to be missing in the literature.…”

Basic notions of (constructive) semigroups with apartness

“…Semilattice decomposition of semigroups is one of the methods with general applications. For more information on semilattice decomposition of semigroups see [19,20]. It is shown in [20] that this method leads to the study of completely isolated and isolated ideals and convex subsemigroups.…”

“…The standard reference for constructive algebra is [18]. For classical semigroup theory see [19,20,22].…”

A Short Note on Bands of Groups

“…In [3], Ciric and S. Bogdanovic studied sturdy bands of semigroups. Then, this concept is studied by many authors, for example see [6,11]. In [7,8,9,10], Lajos studied semilattices of groups.…”