TY  - JOUR
AU  - LIN, Xia
AU  - LI, Changyuan
AU  - LIU, Yuzhe
AU  - ZHAO, Wei
PY  - 2025
TI  - The zero tensor-divisors of 𝕜-algebras
JO  - Journal of Capital Normal University (Natural Science Edition)
SN  - 1004-9398
SP  - 13
EP  - 19
VL  - 46
IS  - 5
AB  - 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.
UR  - https://doi.org/10.19789/j.1004-9398.2025.05.003
DO  - 10.19789/j.1004-9398.2025.05.003