For unital and commutative algebras over an algebraically closed field, any inclusion of finite codimension can be characterised as a chain of inclusions of codimension 1.
 

We investigate the behaviour of such chains when said algebras are ideal subalgebras. That is, when they are sums of the base field with an ideal. So called single clustered polynomial subalgebras can be guaranteed to be contained in a particular type of ideal subalgebra and we provide a means to determine their structure. This characterisation is a direct generalisation of previous results on so called almost monomial subalgebras