I bought a ring  at an import shop, because it fit my finger and
looked nice. It has what appears to be arabic writing on it; I'd like
to know what it says, and maybe the significance of what it says.

A picture of the ring is here:
http://folktale.net/ring.html

Tibetan maybe?  Symbol in lower left could be a stylized AUM.

As Archea here said, this is not Arabic, Tibetian, Hindu or Thai come to mind.

Thanks for the comments.  To narrow it down further, I'm pretty sure
it's not Thai-- I showed it to a Thai exchange student, she didn't
recognise it, but guessed maybe Arabic.

Some of the characters seem to closely resemble a stylized Devan?gar?
alphabet for Sindhi.
 
http://www.omniglot.com/images/writing/sindhi_dev.gif

I could be wrong but I tend to believe the characters on the ring are
more closely tied to Sanskrit or some East Indian origin.

http://www.xs4all.nl/~wjsn/hindi.htm

tutuzdad-ga

its defitnatly not arbic, i speak arbic and have studies quranic arbic
for 7 years which is like ancient arbic, this marking do not even come
close to either one

It means "peace"

Billy Ray Sirus, that's very good news to me, can you tell more?

Some of it resembles Devanagari (Sanskrit alphabet).  That's why I
said the character in the lower left could be AUM.  But the telephone
pole in the upper left doesn't look like any Devanagari character, and
the elongated letters in the middle would have to be not only very
stylized but also built up of multiple characters more than is usual
in Sanskrit.  However, for the purposes of design we see strange
things done to Roman characters all the time and think nothing of it
because we know how to break them down mentally and reform them.  A
native speaker of Hindi could probably tell us if those are really
Devanagari or not.  I said Tibetan because Tibetan characters are
similar to Devanagari, though more angular; but the characteristic
Tibetan forms do not really appear here, so far as my eye can judge.

Archae0pteryx

It also resembles Katakana and Hiragana scripts; both forms of
Japanese Kanji. Some characters do closely resemble the "telephone
pole" character, as it was called earlier.

tutuzdda-ga

Sorry to differ, Tutuzdad, but Hiragana and Katakana aren't forms of
Kanji.  They're different writing systems.  Kanji uses the Chinese
ideographs.  Hiragana is a syllabary invented by a woman because women
weren't allowed to learn Kanji.  Katakana is the same thing, except
that it's used for words that are not Japanese in origin, and many of
the characters are a little or a lot different from the corresponding
Hiragana.  But I don't see any resemblance to Hiragana or Katakana
here.  The characters all hang from a little clothesline like
Devanagari, and I recognize the forms of several individual Sankrit
characters, but not the unusual way they are assembled.  The telephone
pole could be a symbol and not a letter.

By the way, I am not an expert in any of these writing systems or
fluent in their languages, but I have learned to write and
decode--"read" in the sense of being able to say the words aloud as I
read the characters--all three alphabets, Devanagari, Hiragana, and
Katakana, even though I don't understand many of the words they
express.

I'm going to put my money on Devanagari, which is used by several
languages (just as the Roman alphabet is the writing system for many
different languages), double my bet on the AUM, and anticipate
learning that the telephone pole is a symbol that stands for something
(just as we would interpret, say, a cross, a dove, or a star of David,
which are not letters) rather than being part of the written text.

Archae0pteryx

Just another comment saying that it looks like stylized Devanagari:
http://www.geocities.com/Athens/Academy/9594/brahmi.html

Some "Sanskrit words":
http://www.learn-sanskrit.com/sanwords.htm
http://www.learn-sanskrit.com/8limbs.htm

As already mentioned by archae0pteryx-ga the writing on the ring has
nothing to do with Kanji or Kana (Hiragana and Katakana; Katakana
thereby not being only "for words that are not Japanese in origin").