中文摘要：

设k是一个代数闭域，∧=k[x，y]／（x^2，xy，y^3）是一个Gelfand-Ponornarev代数，Ц=（∧~×∧~，rad∧~，0）为其双模问题．本文确定了Mat（Ц）中维数向量为（n，n）的不可分解典范型的结构，并给出了计数公式；定义了Ц上的R-band，证明了Ц上的所有R-band与A的band等价类一一对应，Ц上的不可分解典范型与∧上band-模的同构类一一对应．

英文摘要：

Let ∧ be the Gelfand-Ponomarev algebra G2,3 =k[x,y]/（xy,x^2,y^3）over an algebraically closed field k; let Ц= （∧~×∧~,rad∧~,0） be the bimodule problem of ∧. The present paper determines the structure of the canonical forms of dimension vector （n,n） of A and calculate their numbers; defines a concept of R-band of ∧ and shows that R-bands of ∧ are exactly representatives of equivalent-classes of ∧ bands. Therefore, there is a one-to-one correspondence of parameterized indecomposable canonical forms of Ц and the iso-classes of the band modules of ∧.