Editing Associative algebra (section)

== Non-unital algebras ==

Some authors use the term "associative algebra" to refer to structures which do not necessarily have a multiplicative identity, and hence consider homomorphisms which are not necessarily unital.

One example of a non-unital associative algebra is given by the set of all functions {{nowrap|''f'' : '''R''' → '''R'''}} whose [[limit of a function|limit]] as ''x'' nears infinity is zero.

Another example is the vector space of continuous periodic functions, together with the [[convolution|convolution product]].