ON THE EQUATIONAL THEORY OF PROJECTION LATTICES OF FINITE VON NEUMANN FACTORS

被引：10
|
作者：
Herrmann, Christian [1 ]
机构：
[1] Tech Univ Darmstadt, FB Math, D-64289 Darmstadt, Germany
来源：
JOURNAL OF SYMBOLIC LOGIC | 2010年 / 75卷 / 03期
关键词：
von Neumann algebra; projection lattice; continuous geometry; equational theory; MODULAR LATTICES; WORD PROBLEMS; ALGEBRA; LOGIC; RING;
D O I：
10.2178/jsl/1278682219
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a finite von Neumann algebra factor M. the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(C(nxn)) and is decidable. In contrast, the uniform word problem for the variety generated by all L(C(nxn)) is shown to be undecidable.
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页码：1102 / 1110
页数：9
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