首都师范大学学报（自然科学版）2025，Vol.46Issue(5)：13-19,7.DOI:10.19789/j.1004-9398.2025.05.003
k-代数的零张量因子
The zero tensor-divisors of k-algebras
摘要
Abstract
Let A be a k-algebra defined over a field k.This paper consider the two questions:If the tensor M ⊗ AN on A is zero,under what situation is either M=0 or N=0?If the element,say m ⊗ n,in M ⊗ AN is zero,under what situation is either m=0 or n=0?This study introduces strong/weak zero-tensor-divisors in this paper and provide a solution of the above questions by quiver methods.To be precise,assume that A is a connected algebra whose quiver contains at most one loop,then have the results as follows:(1)A has strong zero-tensor-divisors,the number of vertices of its quiver is greater than or equal to 2,the quiver of A is not a loop.(2)If A does not have weak zero-tensor-divisors then its dimension is infinite.关键词
箭图表示/张量/零张量因子/维数Key words
quiver representations/tensors/zero-tensor-divisors/dimensions分类
数理科学引用本文复制引用
林霞,李长远,刘雨喆,赵伟..k-代数的零张量因子[J].首都师范大学学报（自然科学版）,2025,46(5):13-19,7.基金项目
国家自然科学基金项目(12061001,12171207) （12061001,12171207）
四川省科技厅2023年中央引导地方科技发展项目(23ZYZYTS0335) （23ZYZYTS0335）
贵州大学引进人才科研启动基金项目(贵大人基合字(2022)53号,(2022)65号) （贵大人基合字(2022）
