Fòram na Gàidhlig

I know that the article goes with agam but not with mo, thus an taigh agam but mo bhràthair, but what if the article is already a part of a compound noun? For instance, if "a ring finger" is mac an aba, is "my ring finger" mo mhac an aba or mac m' aba?

I do not know. But my hunch would be "mo mhac an aba". Put it this way: if you had a copy of the book "The Grapes of Wrath", you might refer to it as "my Grapes of Wrath", but not as "The Grapes of my Wrath".

One might even say, I suppose, "am mac an aba agam": something that, at first sight, seems to break all the rules, but is actually OK as "mac an aba" is taken as a fixed expression.

Who was or were "the Queen of Scots' maidservants"?

Hmm, you're probably right. Seems my subconscious is mixing up two totally unrelated concepts here: (1) the rule that you can only have one [definite] article (with possessive pronouns being definite in themselves) and (2) the use of possessive pronouns "in the middle of" compound prepositions, as in air mo beulaibh. The more I think about it the crazier mac m' aba sounds, except (possibly even as) "the son of my abbot"... Tapadh leat!

The Queen of Scots' maidservants? Chan eil mi cinnteach - Beaton, Seaton, Livingston & Flemington?

In x an/na y type nouns, the possessive normally goes into the place of the article/between the nouns (however you want to look at it), cf cùl an dùirn > cùl mo dhùirn, piuthar-athar > piuthar m' athar though in this instance mac m' aba is so laden with ambiguity that I'm fairly certain native speakers would invoke an avoidance strategy (i.e. bend the normal rules) and say mac an aba agam. It's not uncommon, especially in the third person e.g. an t-uchd aige instead of uchd.

Wow, so my subconscious isn't all that crazy after all - now I see it I'm pretty sure I've met with cùl mo dhùirn before. All right, so as rule of thumb, substitution in cases when the phrase is a "literal" compound, eg "my sole" bonn na coise -> bonn mo choise or "your collarbone" cnàimn an uga -> cnàimh d' uga, and avoidance as the lesser evil when it's an "idiomatic" one, eg "their stirrup-cup" deoch an dorais -> deoch an dorais aca?

I think the cutoff is ... oh what's the fancy word that describes when a compound is no longer derivable from its constituents? Like Whitehouse, which you cannot guess from dissecting it into white and house. As opposed to rolling-pin, which you can dissect into rolling + pin to get an idea of what it does?

So cùl an dùirn has a quite literal meaning, back of the hand. But deoch an dorais or mac an aba (as a finger) is pretty distant from the literal meaning so splitting it up is probably something native speakers don't like to do.

I can't remember the fancy word either but I understand, that's what I tried to express by "idiomatic", although I realize that's not exactly the same thing. Anyway, I see the point, mòran taing!

So, just to clarify: going by the examples given, you are adding agam, but omitting the initial article?

tha mac an aba agam goirt, as opposed to tha am mac an aba agam goirt?

i.e. treating the phrase as a unit (a sort of close compound) for the sake of agam, but treating it as discrete items forming a 'genitive chain' as regards only one article?

My instincts (and logic) would incline me to have both the initial article and agam, but I'm not fluent enough to rely on them.

In this case, the "only one article per sequence of nouns" rule hits. The "an" in "mac an aba" is the article. an aba agam -> mac an aba agam.

If the expression was "mac-aba" instead of "mac an aba", then you could have "am mac-aba agam"

Ok, tapadh leat, that's indeed what it looked like.

Tha sin uabhasach... inntinneach!