Lattice Burnside rings
Lattice Burnside rings
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格子伯恩赛德环
DOI：
10.1007/s00012-020-00687-1
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发表时间：
2020
影响因子：
0.6
通讯作者：
and T. Yoshida
中科院分区：
文献类型：
--
作者：
F. Oda;Y. Takegahara;and T. Yoshida
给定一个有限群 G 和一个有限 G 晶格，我们引入了与非空子晶格族相关的晶格 Burnside 环的概念。 Bouc 提出的切片 Burnside 环与格子 Burnside 环同构。任何格子伯恩赛德环都是普通伯恩赛德环的延伸，并且与抽象伯恩赛德环同构。在抽象Burnside环基本定理的基础上探讨了格子Burnside环的环结构。我们探索格子伯恩赛德环素谱的单位群、本原幂等和连通分量。有一些抽象的伯恩赛德环，称为部分格子伯恩赛德环。任何部分格子伯恩赛德环都由格子伯恩赛德环的元素组成。 Bouc提出的截面Burnside环是切片Burnside环的子环，与部分格子Burnside环同构。
Given a finite groupGand a finiteG-lattice, we introduce the concept of lattice Burnside ring associated to a family of nonempty sublatticesoffor. 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.