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中文摘要：
研究了上定向的具有Riesz分解性质的广义效应代数的结构.引入了广义效应代数中素理想的定义,证明了上定向的具有Riesz分解性质的广义效应代数是有限次直既约的当且仅当它是反格;上定向的具有Riesz分解性质的广义效应代数通过理想得到的商代数是反格当且仅当此理想是素理想.最后证明了上定向的具有Riesz分解性质的广义效应代数具有子直积表示.
英文摘要：
The structures of upwards directed generalized effect algebras with Riesz decomposition property are studied.The definition of prime ideal in a generalized effect algebra is introduced.It is proved that an upwards directed generalized effect algebra with Riesz decomposition property is finitely subdirectly irreducible if and only if it is an antilattice.Then it is shown that a quotient of an upwards directed generalized effect algebra with Riesz decomposition property is an antilattice if and only if the ideal inducing that quotient is prime. At last, it is proved that every upwards directed generalized effect algebra with Riesz decomposition property has a subdirect product representation.
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