Trusses: Paragons, ideals and modules
Trusses: Paragons, ideals and modules
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桁架：典范、理想和模块
DOI：
10.1016/j.jpaa.2019.106258
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发表时间：
2019
影响因子：
0.8
通讯作者：
Tomasz Brzezi'nski
中科院分区：
文献类型：
--
作者：
Tomasz Brzezi'nski
本文从环和模理论的观点出发，研究了由分配律连接的具有适当的三元和二元运算的集合-桁架。介绍了桁架中理想和典范的概念，并给出了几种桁架的构造方法。给出了阿贝尔整数群上桁架结构的一个完全分类。定义了桁架上的模，分析了其基本性质和实例。特别地，建立了模的子堆在商堆上诱导出模结构的充要条件。
Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several constructions of trusses are presented. A full classification of truss structures on the Abelian group of integers is given. Modules over trusses are defined and their basic properties and examples are analysed. In particular, the sufficient and necessary condition for a sub-heap of a module to induce a module structure on the quotient heap is established.