Abstract: In this paper，the set of sharp elements in sharply dominating weak commutative pseudoeffect algebras is studied.It’s proved that the set of sharp elements in sharply dominating weak commutative pseudoeffect algebras are weak commutative pseudoorthoalgebras.At the same time，the relationships between weak commutative pseudoeffect algebras and BZ-posets are discussed.At last，it’s proved that the equivalent class of sharp element is sharp element in the quotient algebra of a weak commutative pseudoeffect algebra gotten by normal Riesz ideals.

Key words: sharp elements, weak commutative pseudoeffect algebras, normal Riesz ideals

摘要： 主要研究了由可精确测量元控制的弱可换的伪效应代数中可精确测量元。证明了可精确测量元控制的弱可换的伪效应代数中可精确测量元是弱可换的伪正交代数代数。讨论了弱可换的伪效应代数与BZ-偏序集之间的关系。讨论了弱可换的伪效应代数商代数中可精确测量元与正规Riesz理想之间的关系。

关键词: 可精确测量元, 弱可换的伪效应代数, 正规Riesz理想