@article{LIN2025, 
author = {Xia LIN and Changyuan LI and Yuzhe LIU and Wei ZHAO},
title = {The zero tensor-divisors of 𝕜-algebras},
year = {2025},
journal = {Journal of Capital Normal University (Natural Science Edition)},
volume = {46},
number = {5},
pages = {13-19},
keywords = {quiver representations, tensors, zero-tensor-divisors, dimensions},
url = {https://www.sciopen.com/article/10.19789/j.1004-9398.2025.05.003},
doi = {10.19789/j.1004-9398.2025.05.003},
abstract = {Let    A be a 𝕜-algebra defined over a field 𝕜. This paper consider the two questions: If the tensor    M            ⊗              A        N on    A is zero, under what situation is either    M  =  0 or    N  =  0? If the element, say    m  ⊗  n, in    M            ⊗              A        N 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.}
}