Centrally orthocomplete effect algebras

作者：Foulis David J^*; Pulmannova Sylvia

来源：Algebra Universalis, 2010, 64(3-4): 283-307.

DOI：10.1007/s00012-010-0100-5

• effect algebra
• orthomodular lattice
• boolean algebra
• modular ortholattice
• von Neumann algebra
• JW-algebra
• Loomis dimension lattice
• types I, II, and III

Motivated by the theory of Loomis dimension lattices, we generalize the notion of a hull mapping to an arbitrary effect algebra (EA). Using hull mappings, we identify certain special types of elements in an EA, including generalizations of the invariant elements and of the simple elements in a dimension lattice. We introduce and study a new class of effect algebras, called centrally orthocomplete effect algebras (COEAs), satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. We show that COEAs admit a central cover mapping and we develop the basic theory of direct decomposition of COEAs.

• 出版日期2010-12