his wife is dead and he goes to sell one of the necklaces, only to discover that it is worth a great deal of money. He has, in fact, brought it to the very shop that sold it. He is bewildered and then horribly upset, for he believes that his wife did indeed have a lover.

It is difficult to think of another explanation for Madame Lantin’s possession of such jewelry. The clerks at the jeweler’s shop contribute to the idea of a lover by having a difficult time controlling their laughter. Even the jeweler cannot help but smirk. Monsieur Lantin does, after all, come off looking like a quite a fool, although he ends up very rich in the end.

It is likely that the author does not come right out and say that Madame Lantin has a lover because he would rather allow his readers to find the clues and to discover the secret for themselves. Plus, we have the enjoyment of wondering a bit if we are right or if there could be some other explanation, a secret inheritance or investment perhaps that Madame Lantin used for the jewelry as well as for other expenses around the house. We will never know for sure.

This is an excellent question. Maupassant does not tell the reader whether all the jewelry owned by Madame Lantin came from a single man or from many different men. But this subtle author apparently wished to leave the question a mystery. The story is told from the husband's point of view. He would not necessarily want to know any of the sordid details. It was bad enough for him to realize that his wife had deceived him consistently for years. It would seem that you are quite correct in surmising that Madame was, in a sense, a kept woman. The jewelry she collected is all very expensive. She could not have had a number of lovers who all could afford to lavish such presents on her. It is far more likely that she had one very wealthy lover who was able to adorn her with such tokens of his love. And it must have been genuine love for him to give her so many precious gifts over a long period of time. Nothing would have been gained by the author's naming this invisible figure. And Monsieur Lantin does not want to know.

When Lantin sells the first item, a necklace, to the jeweler from whom it was originally purchased, it is obvious that the jeweler knows the name of the man who originally bought it. In fact, this jeweler probably knows who bought all the jewelry Lantin inherited from his wife, because it is extremely likely that the man who bought the necklace would buy the other things from the same shop. Lantin has no trouble selling all the jewelry to the same jeweler because that man knows them all and knows what prices he sold them for. The following exchange between Lantin and the jeweler shows all this and also shows that Lantin does not want to know the purchaser's name.

As he was about to leave the store, he turned toward the merchant, who still wore the same knowing smile, and lowering his eyes, said:

“I have — I have other gems, which came from the same source. Will you buy them, also?”

The merchant bowed: “Certainly, sir.”

Monsieur Lantin said gravely: “I will bring them to you.” 

The large diamond earrings were worth twenty thousand francs; the bracelets, thirty-five thousand; the rings, sixteen thousand; a set of emeralds and sapphires, fourteen thousand; a gold chain with solitaire pendant, forty thousand — making the sum of one hundred and forty-three thousand francs.

Clearly Monsieur Lantin has a golden opportunity to find out the name of the man who bought all those jewels, because it is obvious that they were all bought from the same jeweler by the same mysterious man. Even if the jeweler refused to identify the customer, it would at least show that Lantin really wanted to find out who it was. But Lantin does not ask because he doesn't want to know. He is humiliated, but he is taking the hundred and forty-three thousand francs and swallowing his pride. 

Madame Lantin was not promiscuous. She was unfaithful to her husband, but at least she was only unfaithful to him with one man. Somehow that seems to make her more respectable. That other man must have given her cash in addition to the jewels.

[Lantin] was unspeakably happy with her. She governed his household with such clever economy that they seemed to live in luxury. 

While Guy de Maupassant certainly could have provided a clear statement regarding Madame Lantin's infidelity in "The Jewelry," it does not necessarily follow that the inclusion of such clarification would have actually improved the story in question. Remember, every decision an author makes while creating a work of fiction is subject to various trade-offs, and Maupassant would not have been an exception.

With that in mind, it may first be worth clarifying that Maupassant (for all that his short stories often revel in ironic turns of fortune) tended to be very much a realist, and, from this perspective, Maupassant's decision-making here does make a certain amount of sense. After all, in real life we are not given all the answers but must grapple with various layers of uncertainty. Thus, the story's ambiguity might actually heighten its sense of realism, mirroring as it does the ambiguities common to lived experience.

Additionally, it might also be argued that this sense of ambiguity actually heightens Lantin's own angst regarding the discovery of the gems. After all, a clear answer on this question (perhaps via the discovery of his wife's correspondence, for example) would provide, if nothing else, a sense of closure. But Maupassant presents a much messier situation than that, one by which Lantin only has suspicions but is not provided a definitive answer one way or the other.