目的给出效应代数水平和的合理定义及研究效应代数上序列积的惟一性。方法利用效应代数、序列效应代数的定义及算子分解的方法。结果在水平和HS(ε(H),[0,1])上存在无穷多个序列积。结论一个效应代数可以具有无穷多个序列积;作为特殊的效应代数-正交代数,能够分解为一些子效应代数的水平和。
Aim To introduce the logical definition of the horizontal sum of effect algebras and study the uniqueness of sequential products on effect algebra. Methods Using the definition of effect algebra, sequential effect algebra and the polar decomposition of operator. Results There exists an infinite number of sequential products on the horizontal sum HS(ε(H), [ 0,1 ] ) of the Hilbert space effect algebra ε(H) and [ 0,1 ]. Conclusion An effect algebra admits an infinite number of sequential products. As a special effect algebra, orthoalgebra can be decomposed to the horizontal sum of sub-effect algebra.