2015/05/03 by Assem, Ali
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1505.00466
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.