JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 6-12.doi: 10.6040/j.issn.1671-9352.0.2023.503

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A note on zero product determined algebras

PAN Shaoze1, SU Shanshan2   

  1. 1. School of Science, Wuxi University, Wuxi 214105, Jiangsu, China;
    2. School of Mathematics, East China University of Science and Technology, Shanghai 200237, China
  • Published:2025-07-25

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Abstract: This paper primarily demonstrates that several classes of algebras possess the property of zero Lie product determinacy. Firstly, it provides some equivalent characterizations of zero product determinacy along with an application. Secondly, we prove that the triangular UHF algebras, countable dimensional locally matrix algebra, and algebras consisting of finite rank operators in J -subspace lattices are all zero Lie product determined. Furthermore, the paper explores the preservationof the zero product determinacy property under certain mappings and presents several counterexamples.

Key words: zero product determined algebra, zero Lie product determined algebra, non-self-adjoint algebra

CLC Number: 

  • O177.1
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