Journal of the Australian Mathematical
Society
J. Aust. Math. Soc.
1446-7887
JAUMA2
2007
83
2
10.wxyz/CV83P2
http://www.austms.org.au/Journal+of+the+Australian+Mathematical+Society/V83P2/
The block structure of complete lattice ordered effect
algebras
Gejza
Jen{č}a
20 February 2008
2008
2
20
181
216
832-b75-Jenca-2007
10.wxyz/C2007V83P2p181
http://www.austms.org.au/Journal+of+the+Australian+Mathematical+Society/V83P2/832-b75-Jenca/
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 $\phi ^*_E:E\to
O(E)$.
primary 06C15; secondary 03G12,
81P10
This research is supported by grant VEGA
G-1/3025/06 of MŠ SR. This work was supported by the Slovak
Research and Development Agency under the contract No.
APVV-0071-06.