English

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

R2 v1 2026-06-22T09:27:19.698Z