Once upon a time, "women's film" was a very popular movie genre. I'm not talking about romantic comedies but rather dramas that were aimed at middle-class and affluent women. Usually they were about wives and their spouses or families. The best known examples here in America are probably the Douglas Sirk melodramas from the 1950's. They were also pretty popular in Japan and here we have what was probably a typical example. An Engagement Ring (the Criterion print on Hulu calls it Wedding Ring) is about a successful business woman played by Kinuyo Tanaka. She is the president of a department store in Tokyo but she has to commute to a remote town every weekend to attend to her husband who has been sick with tuberculosis for years. Trouble arrives in the form of a hunky new doctor, played by Toshiro Mifune.
I have to admit I am not a big fan of the genre. I do like some of Sirk's movies, but this film is nowhere in their league. It does have some nice shots and it is interesting to see Mifune in a rather subdued role. But overall the story is not very compelling and the movie as a whole is rather dull. Completists of old Japanese films or of the director might enjoy it, but I think most people would be rather bored by it.