Genitive -ium

[TeacherPan]

Hello,
I am a secondary education teacher and I teach ancient Greek and Latin. I have a grammar book where I read that all 3rd declension nouns with genitive in -ium have or had stem ending in -i:
e.g.: puppis, puppium
ars [*older nominative: artis], artium.
Also, all neutral nouns have gen. -ium: mare, marium.
Last, there are some analogical formations in -ium: urbs, urbium.

My question: do I have to memorise all nouns with gen. ending -ium, or there's a rule I can use so as to guess when gen. ending is -ium?

[seneca2008]

I hope you find this helpful from from Kennedy's latin primer:

The following rule with regard to the form of the Genitive Plural may be given for practical convenience:
Nouns with a syllable more in the Genitive Singular than in the Nominative Singular (Imparisyllabic Nouns) have Genitive Plural in -um.

Nouns with the same number of syllables in the Nominative Singular and Genitive Singular (Parisyllabic Nouns) have Genitive Plural in -ium.

The chief exceptions to this rule are the following:

(a) Imparisyllabic Nouns which have Genitive Plural in -ium are: glīs, līs, mās, mūs, nox, and Nouns of one syllable of which the Nominative Singular ends in -ns, -rs, -bs, -ps, -rx, -Ix; and neuters in -al, -ar.*

Often also: fraus, rēn, lār, dōs, Nouns of two syllables with Nominative Singular ending in -ns, -rs, and most Nouns in -ās (gen. -ātis). These last and Nouns in -ns are especially variable. Horace writes both parentum and parentium, but the latter is rare.

(b) Parisyllabic Nouns which have Genitive Plural in -um are: canis, iuvenis, senex, sēdēs, pater, māter, frāter, accipiter.f

Sometimes also: apis, mēnsis, vatēs, volucris.

*Nouns of one syllable, of which the Stem has two Consonants before i-, are only apparently Imparisyllabic because the Nom. Sing. originally ended in -is (46), and of some both forms are found; e.g. orbs and orbs. Similarly, neuters in -al, -ar originally ended -āle, āre (47).

fPater, mater, frâter, accipiter, are only apparently Parisyllabic because the e of the Nom. Sing, does not appear in the other cases.

[tico]

Not all neuter names have genitive in -ium: flumen, fluminis -> fluminUM.

[seneca2008]

Not all neuter names have genitive in -ium: flumen, fluminis -> fluminUM.

I think you mean neuter "nouns" rather than "names" and that part of TeacherPan's post is wrong.

But the example of flūmen flūminis confirms the rule of thumb in my post. The genitive flūminis has three syllables compared to the the nominative flūmen's two. So flūmen is Imparisyllabic and so the predicted genitive is flūminum.

[tico]

I think you mean neuter "nouns" rather than "names" and that part of TeacherPan's post is wrong.

Of course, my mistake.

[truks]

where I read that all 3rd declension nouns with genitive in -ium have or had stem ending in -i:

To add to what seneca has written, it's important to remember that i-stems and mixed i-stems will also often behave differently in cases other than the genitive plural.

For instance, some may have an acc. sing. in -im, an abl. sing. in -i and/or an acc. pl. in -is – or show variation between -i- and -e- in some or all of these cases.