Involutorial Płonka sums (Q1410438)

Let \(\mathcal A=(A,F)\) be an algebra. By an involution we mean a unary operation \(*\) on \(A\) such that \((x^*)^*=x\) and it is an antiautomorphism of \(\mathcal A\). Denote by \((A, F, *)\) an algebra with involution. If \(\mathcal A=(A,F)\) is represented as a Płonka sum then the summands need not be subalgebras of \((A,F,*)\). To aviod this difficulty, the authors modify the construction to obtain a very natural so-called involutorial Płonka sum (of an involution semilattice-ordered system of algebras with involutions). Basic properties of this sum are investigated and subdirect decompositions are characterized.