Singular countable nouns without any determiners

Hello,

As far as I know, a singular countable noun must follow a determiner according to English grammar:

  1. englishclub.com/grammar/noun … able_1.htm

However, I found out some singular countable nouns were without any determiners. Could you please explain how they are constructed?

Here are some examples of singular countable nouns used without any determiners:

  1. [oxfordadvancedlearnersdictio … ry/type–(](http://www.oxfordadvancedlearnersdictionary.com/dictionary/type--() a type of house, this type of book).

  2. [dictionary.reference.com/browse/kind--(a](http://dictionary.reference.com/browse/kind--(a) kind of hero, a kind of roof).

Thank you.

Best wishes,
Bhikkhu1991a.

This is called ‘partitive’ construction:

a type/sort/kind of house
a new type of house
New kinds/sorts/types of houses

The article, I suppose, serves for both nouns (‘type’ & ‘house’)

It is the same construction as ‘a piece of cake’, but these latter are partitives of quantity, so are used only with non-count nouns. Partitives of quality (‘a type of’) are used for both sorts of nouns.