One of the books I'm using to study Irish is 'Irish Grammar' by Éamonn ó Dónaill. When discussing noun declensions, this author gives examples of the genitive case which I would consider from studying Latin and other languages as properly belonging to the accusative case. One example is 'ag ní na gcarranna'. I would have expected 'na carranna' to be in the accusative case here, but he says it is in the genitive. Can anyone explain this to me, please?
Many thanks for reading this.

http://www.nualeargais.ie/gnag/subst2.htm#genitivverwend

noun as the object of the verbal noun

* definite noun after the verbal noun:
Tá sé ag déanamh na hoibre = He is doing the work ("He ist at doing the work")
* indefinite noun after the verbal noun, when it has no further attribute:
Tá sé ag cur báistí = It's raining ("it is at laying [a] rain")
* noun with the preposition a (= "zu")that comes before the verbal noun, when the verbal noun itself is the attribute of another nouns (in Ger. most Partizip I); see also verbal noun as an attributive:
fear na mná a phógadh = the man that is kissing the woman ("man that woman to kiss")

Thank you for that, Aonghus. However, to me "ag déanamh" is 'doing', and that's a part of a verb, and 'doing the work' should put 'work' into the accusative case. Surely there is another Irish word for 'the doing' of the work. Surely nouns are preceded by an article in Irish. I am doing 'the washing' would make 'washing' a verbal noun. I am washing would be different. Please convince me that what you say is right, so that I can proceed with my studies.

So I found it, the rule! And that was what I wanted. In an old book, Teach Yourself Irish EUP 1961 by Myles Dillon and Donncha Ó Cróinín:

Lesson VI

"The English present participle is expressed by the preposition ag ,,"at" and a verbal noun;.........and, if there is an object, it appears in the genitive case:....."

Excellent, all I need.

So every time I see the preposition 'ag' before a verbal noun, I use the genitive. Alles klar!

I wouldn't have gone hunting that without your input. Many thanks.

Please refer to page 152 of Irish Grammar where the basic rules are discussed. The object is not always genitive.

It's simple:

Táim ag déanamh na hoibre = literally "I am at the doing of the work". Therefore "déanamh na hoibre" means "the doing of the work". "an obair" must therefore be in the genitive.

quote:

So every time I see the preposition 'ag' before a verbal noun, I use the genitive. Alles klar!

Except when the noun is not a definite noun and is qualified by an adjective or adjectival phrase:

Táim ag déanamh oibre
Táim ag déanamh obair mhaith (good work)

Táim ag déanamh na hoibre
Táim ag déanamh na hoibre maithe (THE good work)

Ailín, you have a knack of pointing rules that sound complex elsewhere simply.

Now I know PUL didn't have to obey the modern rules, and that there is nothing strange if he didn't, but can you comment on whether this would be accepted today.

* ag déanamh oibre sagairt (sagart as an indefinite noun qualifies oibre just as maith qualifies obair in the examples you gave)

Also, I wondered about this:

*ag múineadh an Teagasc Críostaí

Teagasc appears in the nominative. I thought it was because Teagasc was qualified by an adjective, or because the term is viewed as a phrase as a whole, but I don't know for sure why.

Thanks, Seánw.

quote:

Also, I wondered about this:

*ag múineadh an Teagasc Críostaí

maybe because "an Teagasc Criostai" is the title of a book, ie. considered as a proper name...