Aine Ní Mhurchú - Iníon Ní Mhurchú - Áine is single.

Áine Uí Mhurchú - Bean Uí Mhurchú - Áine is married.

Máirtín Ó Cadhain - I thought that this could mean married or single, but I have also seen Máirtín Uí Cadhain so my question is about using Uí for men. Is it that it should be Uí for married men or what's the story?

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Martin Keane (Ó) or Mr. Martin Keane (Uí), I think

Bean Úí is Mrs. follows then

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The ladies won't like this but that's the way the language is -
less to do with a state of being married or single and more to do with ownership I'm afraid!
When a woman marries a man, in Irish she becomes his. Uí is the genitive of Ó.

Bean Uí Mhurchú means the woman of Ó Murchú.

The Uí must be used for anything that belongs to Ó Murchú. So, you will see pubs called Tigh Uí Mhurchú. The Murphy offspring or children will be Clann Uí Mhurchú.

Máirtín Ó Cadhain's book will be leabhar Mháirtín Uí Chadhain.

For the Macs, the genetive is Mhic.
Bean Mhic Cárthaigh. ['c' and 'g' are normally not lenited after Mhic or Nic]
Dán Phádraig Mhic Phiarais = Patrick Pearse's poem.

I was taught the exact opposite:
Bean means "woman", and bean also means "wife".
Fear means "man", and fear also means "husband".

So, Bean Uí Mhurchú means "wife of Ó Murchú" and has nothing to do with ownership, just like using the word fear for "husband" has nothing to do with being owned.

From page 131 of Teach Yourself Irish (the original version by Dillon and Ó Cróinín):
"A married woman does not take the surname of her husband. If Mary Kelly marries Peter O'Sullivan, she remains Máire Ní Cheallaigh or may be called bean Pheadair Uí Shúilleabháin, but not Máire Ní Shúilleabháin." That's why Peig Sayers' name, for example, didn't change when she got married. The whole notion of "owning" somebody in marriage is a foreign concept to Gaelic Ireland.

Dia duit, WFM agus Athbhliain faoi shéan is faoi mhaise duit.
Can I say firstly that I have no wish to get into an argument about what was or was not a foreign concept in Gaelic Ireland. Everyone will make his/her own claims regarding that.
My point is a grammatical one - and your own use of 'of' (when you say wife 'of' and husband 'of') above consolidates that point: Uí is the genitive of Ó.
The only difference between your sentence and what I wrote is that you use husband and wife where I used man and woman. I expect that the words husband and wife only came in with Christianity and would submit that Gaelic Ireland was in existence before that. All these are small points in my opinion.
I think that Dillon and Ó Cróinín are trying to ensure that people do not use 'Ní' for a woman's surname after she gets married (assuming she takes her husband's surname). 'Ní' comes from 'iníon' meaning daughter and thus would be totally wrong to use with a spouse's surname. It was and is used with the father's surname. If a woman decides to keep her maiden name after getting married, then of course she would use 'Ní' along with her father's surname - Ní Cheallaigh in the example above. But if she chooses to use her husband's surname she has to use 'Uí' which, like it or not, is the genitive of 'Ó'.

Taking your husbands surname was adopted in Ireland from the English custom. In medieval to early modern Gaelic Ireland, women kept their own surnames. Dillon and Ó Cróinín are essentially conveying that this was still practised in the Cork Gaeltacht in the 1950s.

Things like Máire Uí Mhurchú are not to be found until the 19th/20th century, and arose as attempt to copy the English language "Mrs. Murchú".

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

Dia is Muire dhuit agus athbhlian fé shéan agus fé mhaise duit-se. I'm not trying to get into an argument either, and I sure hope that I didn't come across that way.
Tá an ceart agat, a Loin Dhuibh! – that's exactly what I was taught

Also I was taught that bean cheile and fear cheile meant simply the person you were romantically involved with and not neccessarily married to

Me neither, WFM.
And sorry, I should have said discussion rather than argument.

By the way, I'm not disagreeing with yourself or Lon Dubh. I accept that the use of Uí to denote Mrs has come about in recent centuries through the anglicisation process - as it has in other cultures that have been influenced by the English bureaucratic system, I believe. I'm grateful to both of you for pointing that out. My point is that linguistically it is the genitive of Ó and is used in the ownership sense in the language. While I would be delighted if my own daughter were to decide when/if the time comes that she intends to keep my surname rather than take that of her husband, I don't see the culture of women keeping their maiden names returning any time soon. I could be wrong of course.
My main interest in posting was to try to help those that posed the question regarding the link between Uí and the surnames of married people and whether it is used in that sense with mens' married surnames. My point is that linguistically Uí is the genitive of Ó and is used for what belongs to the man, accepting that the concept of a woman belonging to a man has come in from English culture. For that reason, you won't get the likes of 'Seán Uí Ghríofa' as a stand alone but rather, after the noun that he "owns" - gluaisteán Sheáin Uí Ghríofa, páiste Sheáin Uí Ghríofa or indeed, in present use Bean Sheáin Uí Ghríofa.

Guím gach rath oraibh in 2014 - go raibh tuilleadh plé againn ar ghnéithe éagsúla den teanga i rith na bliana.
Le gach beannacht,

Muimhneach

Weren't surnames introduced/forced by the English?

The Irish traditional naming is "John, son of Michael, grandson of Martin etc"
Nan Tom Taimín;
Bríd Choilimín Antaine;

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It is recommended that you always wait for three to agree on a translation.
I speak Connemara Irish, and my input will often reflect that.
I will do an mp3 file on request for short translations.
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