Abstract. In order to explore the submodules in the Hardy space over the bidisk, a new equivalence relation which is based on the core operator, namely congruence, was introduced in [Yan2005]. As we know, the structure of the submodules in $H^2(\mathbb{D}^2)$ is very complicated. So it is beneficial to study some good examples of submodules. This paper studies the congruence of the Hardy submodule over the bidisk. It will be shown that the congruence of two inner sequences based submodules can be totally described by the ratio of their inner sequences.

DOI: 10.14232/actasm-016-550-y

AMS Subject Classification (1991): 47A13, 46E20

Keyword(s): core operator, congruence, inner sequence based submodule

Received September 16, 2016, and in revised form November 16, 2016. (Registered under 50/2016.)