@article{Martín2026, 
author = {Antonio J. Calderón Martín},
title = {On the decomposition of perfect arbitrary algebras as a direct sum of indecomposable ideals},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14840-14856},
keywords = {arbitrary algebra, decomposition, indecomposable ideal, perfect algebra, linear group, structure theory},
url = {https://www.sciopen.com/article/10.3934/math.2026611},
doi = {10.3934/math.2026611},
abstract = {We consider perfect algebras    A  (that is,        A    2    =  A), in their greatest generality. That is, of arbitrary dimension, over an arbitrary base field, and no identity or condition are assumed for the product. We introduce a certain action involving the linear group of    A and provide a characterization and a necessary condition for    A, in terms of the above action, to be a direct sum of indecomposable ideals.}
}