A non-capped tensor product of lattices

被引：1
|
作者：
Chornomaz, Bogdan [1 ]
机构：
[1] Kharkov Natl Univ, Dept Comp Sci, Kharkov, Ukraine
来源：
ALGEBRA UNIVERSALIS | 2014年 / 72卷 / 04期
关键词：
tensor product; semilattice; lattice; capped lattice; SEMILATTICES;
D O I：
10.1007/s00012-014-0304-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In lattice theory, the tensor product is naturally defined on (, 0)-semilattices. In general, when restricted to lattices, this construction will not yield a lattice. However, if the tensor product is capped, then is a lattice. Whether the converse is true is an open problem, first posed by G. Gratzer and F. Wehrung in 2000. In the present paper, we prove that it is not so, that is, there are bounded lattices A and B such that is not capped, but is a lattice. Furthermore, A has length three and is generated by a nine-element set of atoms, while B is the dual lattice of A.
引用
收藏
页码：323 / 348
页数：26
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