@article{Cheng2021, 
author = {Daizhan Cheng and Zhengping Ji and Jun-e Feng and Shihua Fu and Jianli Zhao},
title = {Perfect hypercomplex algebras: Semi-tensor product approach},
year = {2021},
journal = {Mathematical Modelling and Control},
volume = {1},
number = {4},
pages = {177-187},
keywords = {semi-tensor product (STP) of matrices, perfect hypercomplex algebra (PHA), zero-set},
url = {https://www.sciopen.com/article/10.3934/mmc.2021017},
doi = {10.3934/mmc.2021017},
abstract = {The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed. The zero sets are defined for non-invertible hypercomplex numbers in a given PHA, and characteristic functions are proposed for calculating zero sets. Then PHA of various dimensions are considered. First, classification of  2-dimensional PHAs are investigated. Second, all the  3-dimensional PHAs are obtained and the corresponding zero sets are calculated. Finally,  4- and higher dimensional PHAs are also considered.}
}