The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
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DOI：
10.1007/s00500-010-0561-7
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发表时间：
2011-03
期刊：
影响因子：
4.1
通讯作者：
Jan Paseka;Z. Riecanová
中科院分区：
文献类型：
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作者：
Jan Paseka;Z. Riecanová
本文研究了阿基米德原子格效应代数E的显著子格效应代数，即E的块M、中心C（E）、相容中心B（E）和所有尖元S（E）的集合。我们证明了在每一个这样的效应代数E中，每一个原子块M和集合S（E）都是E的双满子格效应代数。因此，如果E是进一步的严格支配，那么每个原子块M再次是严格支配的，并且E和M中元素的基本分解（BDE of x）是一致的。因此，在E的相容中心B（E）中，非零元素以中心元素为主，它们的基本分解与所有原子块和E中的基本分解一致。一些进一步的细节，这可能是有帮助的答案下的存在性和属性的状态。即证明了每个锐控制的阿基米德原子格效应代数E上存在一个（o）-连续态，并证明了对于紧生成的阿基米德格效应代数，态的（o）-连续性与其完全可加性是等价的.进一步，我们证明了这些格效应代数的“状态涂抹定理”。
We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebrasE, namely their blocksM, centersC(E), compatibility centersB(E) and sets of all sharp elementsS(E) ofE. We show that in every such effect algebraE, every atomic blockMand the setS(E) are bifull sub-lattice effect algebras ofE. Consequently, ifEis moreover sharply dominating then every atomic blockMis again sharply dominating and the basic decompositions of elements (BDE ofx) inEand inMcoincide. Thus in the compatibility centerB(E) ofE, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks and inE. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely, we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebraEwithMoreover, for compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved. Further, we prove “State smearing theorem” for these lattice effect algebras.