Pronunciation: [ɐdˈɛlɪk] (IPA) 
The word "adelic" is spelled phonetically as /əˈdɛlɪk/. The first sound, /ə/, is a neutral vowel called a schwa. The next sound, /ˈdɛl/, represents "del," which is pronounced as in "delight" or "dell" as in a valley. The final sound, /ɪk/, represents "-ic," which means "pertaining to" and is pronounced as in "magic" or "topic." Therefore, "adelic" is a word meaning "pertaining to or resembling a noble or aristocratic family line."
Adelic is an adjective that refers to a mathematical concept within the field of number theory known as adeles. Adeles are a generalization of the concept of an algebraic number, representing a collection of all possible valuations of a number at each place (both finite and infinite) in a given number field. The term "adelic" describes properties or ideas related to adeles.
In a more specific sense, the term "adelic" is often used to describe certain arithmetical or geometric ideas that are associated with adeles. It can refer to mathematical operations, structures, or theorems that involve the use of adeles. For example, one might encounter discussions of adelic representations or adelic groups in the study of automorphic forms or the Langlands program.
The notion of adeles and adelic ideas has found extensive applications in various areas of mathematics, such as number theory, algebraic geometry, and representation theory. These concepts provide a powerful framework for studying the interactions between different number fields and their associated places, leading to deeper insights into the behavior of numbers and the connections between seemingly unrelated mathematical objects.
In summary, adelic is a term used to describe mathematical concepts, operations, or theorems that are associated with adeles - a generalization of algebraic numbers that captures the valuations of a number at each place in a field.
