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中文摘要：
[中国科学A，2011，41（3）：279—286]引入了效应代数的表示，给出了可表示与不可表示的效应代数的例子，证明了某些效应代数的可表示性．然而，尚未得到一般效应代数的可表示准则，基于抽象C＊-代数的GNS构造的思想，我们猜测具有足够多的态的抽象效应代数应当是可以表示的．因而，态的存在性与态空间的表示问题对于建立抽象效应代数的表示理论、解决分类问题似乎是至关重要的．本文讨论效应代数上态的存在性和赋值的存在性问题，给出了若干典型的效应代数上态的一般形式与它们的态空间．特别地，证明了可表示效应代数上态的存在性定理，并得到了到态空间与赋值空间的非空凸子集．
英文摘要：
Representations of abstract effect algebras was introduced in the literature [Sci. Sin. Math., 2011, 41（3）： 279-286], some examples of representable effect algebras and unrepresentable effect algebras were given there. However, a general criterion about the representations of effect algebras was not obtained. Based on the idea of the GNS structure of an abstract C＊-algebra, we guess that abstract effect algebras admitting much enough states should be representable. Thus, the existence of states and the representations of state spaces seem to be important in the representation theory and the classification problem of abstract effect algebras. This paper is devoted to discussing the existence of states and valuations of effect algebras. General forms of states and state spaces of some typical effect algebras are obtained. EsPecially, the existence theorem of states of representable effect algebras is proved and nonempty convex subsets of state space and valuation space of an effect algebra are given, respectively.
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