Algebraic coalitions. II (Q5932472)

The paper is a continuation of the author's earlier work [Algebra Univers. 38, 1-14 (1997; Zbl 0903.08012)]. Here the notions of algebras in \(\mathcal S \mathcal E \mathcal L \mathcal F\) and of coalition were introduced and studied for the case of any congruence modular variety or any variety of Jónsson-Tarski algebras. One motivation for their study is that algebras in \(\mathcal S\mathcal E \mathcal L \mathcal F\) give a nice measure for an algebra to be abelian. For a variety \(\mathcal V\), a \(\mathcal V\)-algebra in \(\mathcal S \mathcal E \mathcal L \mathcal F\), \(\langle R,\circ ,\text{id}\rangle \) consists of a \(\mathcal V\)-algebra \(R\) that is enriched by the addition of a binary function \(\circ \) and a distinguished element id of \(R\) that is a two-sided identity for \(\circ \), which are both respected by the operations of \(R\). In the earlier work it has been shown that in the case when \(\mathcal V\) is a congruence modular variety or a variety of Jónsson-Tarski algebras any given \(\mathcal V\)-algebra has a coalition center. The purpose of the present paper is to show that this fact holds also for the variety of semilattices, the variety of inverse semigroups and any subtractive variety.