Abstract This paper is devoted to the study of the class of decomposable double MS-algebras. Necessary and sufficient conditions for a decomposable MS-algebra to be a decomposable double MS-algebra are deduced. We construct decomposable double MS-algebras by means of decomposable MS-quadruples and we prove that there exists a one-to-one correspondence between decomposable double MS-algebras and decomposable MS-quadruples. Moreover, a construction of decomposable K2-algebras (Stone algebras) by means of K2-quadruples (Stone quadruples) is given. We conclude by introducing and characterizing isomorphisms of decomposable double MS-algebras in terms of decomposable MS-quadruples.

中文翻译：

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可分解双 MS-代数的四重构造

摘要 本文致力于研究一类可分解的双MS-代数。推导出可分解的MS-代数成为可分解的双MS-代数的充要条件。我们通过可分解的 MS-四元组构造了可分解的双 MS-代数，并证明了可分解的双 MS-代数和可分解的 MS-四元组之间存在一一对应的关系。此外，还给出了通过 K2-四元组（Stone quadruples）构造可分解的 K2-代数（Stone algebras）。我们通过根据可分解 MS-四元组介绍和表征可分解双 MS-代数的同构来得出结论。