Gemara

(Beraisa): One may go out with a bell on his garment, but not on his neck.

Question: Why is a bell on his neck forbidden?

Presumably, we are concerned lest it fall and he will carry it. The same applies to a bell on his garment!

Answer: The case is, it is woven into the garment. (Surely, it will not fall);

(Rav Huna brei d'Rav Yehoshua): Anything woven is permitted.

62b (Beraisa - R. Meir): A woman may not go out with a key in her hand. If she did, she is Chayeves Chatas.

139b (R. Avin bar Rav Huna): One may cloak himself in a Kilah (a canopy normally spread over a bed) and walk in Reshus ha'Rabim, without concern for the straps [used to hang it. They are not considered a load.]

Question: Why is this different than Rav Huna's law?

(Rav Huna): If one walks in Reshus ha'Rabim on Shabbos with Tzitzis that do not fulfill the Mitzvah, he is Chayav Chatas. (They are like a load!)

Answer: [Even invalid] Tzitzis are important. They are not Batel to the garment. Straps are Batel to the Kilah.

Rishonim

Rosh (6:10): The Yerushalmi brings an episode in which R. Gamliel entered his Chatzer on Shabbos holding a gold key. His colleagues rebuked him due to [an ornament]. This shows that if it is made for an ornament, it is forbidden, and even if it is for an ornament and for use, and the same applies to a man or woman. Also, even when it is forbidden (to take it out on Shabbos to Reshus ha'Rabim) and one is not liable, it is forbidden even in a Chatzer. (The Rif says so.) The Ba'al ha'Ma'or rejected this proof. A key is different, for it is an ornament for a man and woman, therefore Chachamim did not distinguish men from women. Something that is an ornament for a man and not for a woman is permitted. The Ramban defended the Rif. The Yerushalmi initially asked 'is a man permitted because he does not show off his ornaments?!', and brought the episode with R. Gamliel to refute this. It asked about men's ornaments, and learned from ornaments for everyone, without distinction. I (the Rosh) say that the questioner rejected the answer. 'What is for this and this' means 'for a man or woman.' Some say that it means 'for an ornament and for use', e.g. a key to open a lock, is forbidden for a man or woman, for onlookers will say that he took it out for use. R. Shmuel ha'Nagid said so. We do not decree regarding men lest they show off ornaments. In Ashkenaz they make keys, and women hang them from their necks with silver chains or colored threads, and go out with them.

Rashba (3:262): Some villagers made a key at the end of their belts. They take it out[side], and think that it is Batel to the belt. I forbade this. Any item not needed for a Kli, it does not serve the Kli, and it is not Batel to it. It is as if one is Motzi (takes out) the item by itself, without the Kli [even if it is attached to it]. We learn from Shabbos 139b. We say that straps of the Kilah are Batel to the Kilah, for they are not important by themselves. Pasul Tzitzis are important by themselves. They are not Batel to the garment. The same applies to a key in a belt. It was not placed there for use of the belt, rather, for its own use. It is not Batel to the belt. One who takes it out on Shabbos is Chayav Chatas.

Beis Yosef (OC 301 DH veha'Rashba): Based on this, even if it is of silver one is Chayav Chatas. In any case we can find a Heter when it is of silver, for it itself is an ornament.

Hagahos Maimoniyos (19:4, on Halachah 8, citing Maharam): Some people fix a key of iron or other metals in their belt, for Noy. On Shabbos they use it to lock and open. This is unlike bells, which we permit. We established this to be when they are plugged up. Even if you will say that fixing a key in a belt is like plugging up a bell, we permit only a bell, which they used to put in all garments for Noy. They did not exert people to remove them [for Shabbos] and mar the garment. This is why Chachamim distinguished and forbade a signet, even though it is woven [for it is not common]. It is not common to fix keys in a belt. Even if it is woven and fixed, we can say that it is as if it is detached. We can even say that it is like a load. We say that one who goes out with a key is Chayeves Chatas. Perhaps the same applies here. Perhaps the key is not Batel to the belt, rather, the belt is Batel to the key! One who goes out with Tzitzis that are not Kosher is liable. One should permit only through clear proofs. Also, if such a case were permitted, early Chachamim would not have needed to find a Heter through keys of silver or gold or through chains or straps of silver or gold, e.g. chains to insert in the lapels of the cloak, which is Derech Tachshit (ornamental). If one can make an iron key, why was this needed? Even though I heard that some are lenient, but I don't know their source. Mar brei d'Ravina did not authorize this.

Beis Yosef (ibid. DH u'Mah she'Chasav sheha'Ram): Also the Mordechai (350) brought like this in the name of Maharam. Hagahos Maimoniyos clearly holds that Maharam forbids only if it is of iron or copper or similar things, but permits of silver or gold. The Rosh said similarly about his Rebbeyim in a Teshuvah (22:11).

Maharil (84, 157:13, cited in Beis Yosef DH uvi'Teshuvah): If a silver key is fixed in a belt, if it is an ornament for a woman, even if it is of iron, people permit, like R. Peretz and the Agudah, even though Maharam censured this. Meticulous people connect it through a silver peg. Those who permit consider it like an ornament of the belt, like a (bell) woven into his garment when it is plugged up. Chachamim did not decree about anything woven. Maharam disagreed. The custom is to be lenient, for not everyone can make it of silver. It seems that Maharam agrees about silver, even though according to some Perushim of the Rosh, the Yerushalmi distinguishes between men and women regarding the gold key of R. Gamliel. It was not attached to the belt.

Beis Yosef (ibid.): We did see anyone lenient about this. We are stringent.

Poskim

Shulchan Aruch (OC 301:11): If something is made for an ornament and a use, e.g. beautiful silver keys that are like ornaments, it is forbidden [to take it out on Shabbos], for onlookers will say that he takes it out for use.

Mishnah Berurah (41): Even if he intends to hang it on the neck for an ornament and Noy, it is forbidden due to onlookers. This is even according to R. Tam and the Rambam, who permit an ornament for a man. (The other opinion forbids according to letter of the law, even without concern for onlookers.) Or, [letter of the law it is permitted because] the key is fixed well in a chain on his neck, and it is hard to take it off to show it. Even so, it is forbidden due to onlookers.

Shulchan Aruch (ibid.): Some permit if it is of silver.

Mishnah Berurah (42): Since it is not normal to make a key of silver, it is primarily for an ornament. Even though they also use it, it is permitted when he takes it out for an ornament. If it is of iron or copper, even if it is made like an ornament, one may not go out with it, since it is primarily for use. Most keys are of iron or copper. The Shulchan Aruch connotes like the first opinion, since he wrote so Stam. (He did not say 'some say...') In any case we do not protest, since the Darchei Moshe brought from the Agur that in Ashkenaz they permit silver keys.

Kaf ha'Chayim (62): it is permitted only when it is attached in the belt or on a chain from the neck, so a woman could not remove it and show it off. If not, it is an ornament for a man or woman, and even a man may not go out with it. The Levush, Bach and Olas Shabbos say so. Eliyahu Rabah infers that they hold like those who permit. However, Me'orei Ohr says that we see that it is not an ornament for a man, so even for a woman we permit only for a need.

Rema: In any case one may not go out with a case for eyeglasses, even if it is of silver, since the glasses themselves are a load. If the key is of copper or iron, even if it is attached and fixed in the belt, it is forbidden.

Beis Yosef (DH u'Mah she'Chasav u'Lfi): According to those who explain that 'what is for this and this' means 'for an ornament and for use', surely keys that are ornaments and for use are forbidden, like the Tur says. However, the Rosh connotes that he explains that it means 'for a man or woman.' It was never taught that something for an ornament and for use is forbidden, so it is permitted. That is why he said that in Ashkenaz they permit, and he did not argue. Also Semag, Semak, Sefer ha'Terumah and Hagahos Maimoniyos say that rich women take out gold or silver keys with a needle to close the flaps of the garment at the neck. I.e. one end is pointy like a needle, and the other end is thick and used for a key. According to them, R. Gamliel's colleagues rebuked him because he held it in his hand. In such a case, regarding women there is concern lest they show it off. Since it is an ornament also for a woman, and it is forbidden for her, it is forbidden also for a man. The custom in Ashkenaz is that the key is tied to the neck. There is no concern, for she can show it without removing it. Also, it is not so easy to remove it. Therefore, it is permitted even for a woman.

Taz (7): If the key is of silver, or hangs from a silver chain, the Rosh permits. This connotes that even an iron key hanging from a silver chain is permitted. The key is Batel to the chain.

Kaf ha'Chayim (68): Tosefes Shabbos (25) says that we do not make a key for a chain! (Rather, the chain is Batel to the key.) The Rosh permits only when the key is of gold [or silver - PF].

Gra (DH v'Im): If a woman goes out with a key in her hand [she is Chayeves Chatas]. This means that it is on her finger, like it says in the Yerushalmi.

Shulchan Aruch (ibid.): Some say that the custom is to permit.

Magen Avraham (18): It is permitted only when it is at the end of the belt, and used [for a buckle] to gird. If it is in the middle, it is forbidden.

Gra (DH Afilu): The lenient opinion considers this like a bell. Chachamim did not decree against anything woven. Others rejected this, for if so, even a signet should be permitted!

Kaf ha'Chayim (69): If it is loose and there is concern lest it fall and one will carry it four Amos in Reshus ha'Rabim, it is forbidden even if it is an ornament.