What is an associative array abstract data type?

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From the web, I got the definition of a HashMap as:

In computing, a hash table (hash map) is a data structure which implements an "associative array abstract data type", a structure that can map keys to values. A HashTable uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found.

Now my question is that what is the proper meaning of the quoted line: "associative array abstract data type"?

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associative array is an array that instead of indexes it is being accessed by keys which could be integers, but also could be strings and other types. Or in other words... a Map/Dictionary (it's a synonym).

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Associative arrays are also called as Map/Symbol table/Dictionary, which is an abstract data type (a data type which is defined by its behavior), and it is a collection of (key, value) pairs and each key here appears at most once. I hope this helps.