论文标题
具有非循环SOCLE和扩展属性的模块
Modules with Non-Cyclic Socle and the Extension Property
论文作者
论文摘要
2009年，J。Wood证明了Frobenius Bimodules具有对称重量组成的扩展特性。更普遍的是，后来表明，具有循环的Socle足以满足该财产，而必要性仍然是一个空旷的问题。在本文中，证明了部分匡威。对于一类重要的有限模块字母，为满足扩展特性所必需的环状条件是必要的。这个想法是使用新的重量功能返回到锤重的原始情况。
In 2009, J. Wood proved that Frobenius bimodules have the extension property for symmetrized weight compositions. More generally, it was later shown that having a cyclic socle is sufficient for satisfying the property, while the necessity remained an open question. In this thesis, a partial converse is proved. For a significant class of finite module alphabets, the cyclic socle condition is shown necessary for satisfying the extension property. The idea is to use a new weight function to return to the original case of Hamming weight.
