J. Aust. Math. Soc. 83 (2007), no. 2, pp. 181–216.

The block structure of complete lattice ordered effect algebras

Gejza Jenča
Department of Mathematics
Faculty of Electrical Engineering and Information Technology
Ilkovičova 3
812 19 Bratislava
Slovakia
gejza.jenca@stuba.sk
Received 4 May 2005; revised 28 June 2006
Communicated by M. Jackson
This research is supported by grant VEGA G-1/3025/06 of MŠSR. This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0071-06.

Abstract

We prove that every for every complete lattice-ordered effect algebra E there exists an orthomodular lattice O(E) and a surjective full morphism \phi _E:O(E)\to E which preserves blocks in both directions: the (pre)image of a block is always a block. Moreover, there is a 0,1-lattice embedding \phi ^*_E:E\to O(E).

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2000 Mathematics Subject Classification: primary 06C15; secondary 03G12, 81P10
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