n阶三角矩阵环上的有限嵌入模

Finitely embedded modules over triangular matrix rings of order n

设Γ是一个n阶三角矩阵环,其中n≥2是一个整数。给出了一个Γ-模的子模是本质子模的等价刻画与一个Γ-模的基座具体形式。特别地,作为上述结论的运用,给出了一个Γ-模是有限嵌入模的充分必要条件。

Let Γ be a triangular matrix ring of order n,where n≥2 is an integer. The equivalent characterization of a Γ-module whose submodule is an essential submodule,and the concrete description of the socle of a Γ-module are given. In particular,as an application of the above conclusion,a necessary and sufficient condition for a Γ-module to be a finitely embedded module is given.