Quadruple construction of decomposable doubleMS-algebras
Abd El‐Mohsen Badawy, S.E.S. Hussein, Ahmed Gaber · Mathematica Slovaca · 2020
Abstract This paper is devoted to the study of the class of decomposable doubleMS-algebras. Necessary and sufficient conditions for a decomposableMS-algebra to be a decomposable doubleMS-algebra are deduced. We construct decomposable doubleMS-algebras by means of decomposableMS-quadruples and we prove that there exists a one-to-one correspondence between decomposable doubleMS-algebras and decomposableMS-quadruples. Moreover, a construction of decomposableK2-algebras (Stone algebras) by means ofK2-quadruples (Stone quadruples) is given. We conclude by introducing and characterizing isomorphisms of decomposable doubleMS-algebras in terms of decomposableMS-quadruples.