Given a finite group G and a finite G-lattice \({{\mathscr {L}}}\), we introduce the concept of lattice Burnside ring associated to a family of nonempty sublattices \({{\mathscr {L}}}_H\) of \({{\mathscr {L}}}\) for \(H\le G\). The slice Burnside ring introduced by Bouc is isomorphic to a lattice Burnside ring. Any lattice Burnside ring is an extension of the ordinary Burnside ring and is isomorphic to an abstract Burnside ring. The ring structure of a lattice Burnside ring is explored on the basis of the fundamental theorem for abstract Burnside rings. We explore the unit group, the primitive idempotents, and connected components of the prime spectrum of a lattice Burnside ring. There are certain abstract Burnside rings called partial lattice Burnside rings. Any partial lattice Burnside ring consists of elements of a lattice Burnside ring. The section Burnside ring introduced by Bouc, which is a subring of the slice Burnside ring, is isomorphic to a partial lattice Burnside ring.

给定有限群G ^和有限ģ -lattice \（{{\ mathscr {L}}} \） ，我们引入晶格伯恩赛德环的关联到一个家庭非空亚晶格的概念\（{{\ mathscr {L}} } _H \）的\（{{\ mathscr {L}}} \）为\（H \文件ģ\）。Bouc引入的片状Burnside环与晶格Burnside环同构。任何晶格的伯恩赛德环都是普通伯恩赛德环的扩展，并且与抽象伯恩赛德环同构。在抽象伯恩赛德环的基本定理的基础上，研究了晶格伯恩赛德环的环结构。我们探索了晶格伯恩赛德环的素谱的单位群，原始幂等数和连通分量。有某些抽象的Burnside环称为部分晶格Burnside环。任何部分晶格伯恩赛德环均由晶格伯恩赛德环的元素组成。Bouc引入的截面Burnside环是切片Burnside环的子环，它与部分晶格Burnside环同构。