A Characterization of Modules with Cyclic Socle
Rings and Algebras
2015-05-05 v1
Abstract
In 2009, J. Wood [15] proved that Frobenius bimodules have the extension property for symmetrized weight compositions. Later, in [9], it was proved that having a cyclic socle is sufficient for satisfying the property, while the necessity remained an open question. Here, landing in Midway, the necessity is proved, a module alphabet RA has the extension property for symmetrized weight compositions built on AutR(A) is necessarily having a cyclic socle.
Keywords
Cite
@article{arxiv.1505.00466,
title = {A Characterization of Modules with Cyclic Socle},
author = {Ali Assem},
journal= {arXiv preprint arXiv:1505.00466},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1412.6083