Г-环的单位元

On the Unity in Γ-rings

中文摘要:

      Γ-环的乘法单位元比结合环的乘法单位元更复杂,更富有变化.首先它有单位元,α-单位元(强单位元)之分,其次它具有与结合环单位元相异的性质,对此本文逐一阐述.此外还探讨了Γ-环M与其矩阵环M_m,n单位元间的关系.在导入Γ-环的特征这一概念后,证明了具有单位元Γ-环的特征的一些性质.

英文摘要:

      The unity for multiplication in Γ-rings is more complicated and changeful than that in associative rings. First it is classified to be unity or a-unity (strong unity). Secondly it possesses different properties with that in associative rings. These properties are expounded in this paper. The relation between the unities in Γ-ring M and in its matrix ring M_m,n is studied. This relation has feature of Γ-rings too. Lastly the characteristic chM of Γ-ring M is introduc-ed, Some properties of chM are proved for M with unities.