桁架：典范、理想和模块
Trusses: Paragons, ideals and modules
摘要：
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运算和二元运算的桁架。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。给出了整数阿贝尔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分和必要条件。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
